Osaka City University Advanced Mathematical Institute
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Department of Mathematics and Physics
Graduate School of Science
Osaka City University
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Organizer in 2014 : Shin'ya Okazaki |
Dept. of Mathematics moved to Science Building.
Campus Map
Science is No. 12.
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Speaker |
:Akihiko Sato (Nagoya University) |
Title |
:Daikoku-Sakai-Takase move for links |
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(Abstract)
(PDF) |
Date |
:February 22 (Sun.) 16:00~17:00 |
Place |
:Dept. of Mathematics, Sci. Bldg., F404 |
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Top |
Speaker |
:Takurou Sakamoto (Nagoya University) |
Title |
:Quantum link invariant of G_2 quantum group
and the fundamental representations |
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(Abstract)
(PDF) |
Date |
:February 22 (Sun.) 15:00~16:00 |
Place |
:Dept. of Mathematics, Sci. Bldg., F404 |
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Top |
Speaker |
:Atsushi Ishii (Tsukuba University) |
Title |
:The Markov theorem for spatial graphs with Y-oriented IH-labeled
spatial trivalent graphs |
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(Abstract)
(PDF) |
Date |
:January 16 (Fri.) 16:30~17:30 |
Place |
:Dept. of Mathematics, Sci. Bldg., F404 |
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Top |
Speaker |
:Sukuse Abe (Saitama University) |
Title |
:Definition of finite type invariants of connected oriented
compact 3-manifolds |
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(Abstract)
(PDF) |
Date |
:January 9 (Fri.) 16:30~17:30 |
Place |
:Dept. of Mathematics, Sci. Bldg., F404 |
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Top |
Speaker |
:Hitoshi Murakami (Tohoku University) |
Title |
:The volume conjecture and its generalizations |
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(Abstract)
(PDF) |
Date |
:December 12 (Fri.) 16:30~17:30 |
Place |
:Dept. of Mathematics, General Research Bldg., 401 |
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Top |
Speaker |
:Alexander Zupan (University of Texas at Austin) |
Title |
:Surface knots with small bridge number |
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(Abstract)
(PDF) |
Date |
:December 5 (Fri.) 16:30~17:30 |
Place |
:Dept. of Mathematics, General Research Bldg., 401 |
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Top |
Speaker |
:Shumi Kinjo (Shinshu University) |
Title |
:Immersions of 3-sphere into 4-space associated with Dynkin
diagrams of types A and D |
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(Abstract)
(PDF) |
Date |
:November 28 (Fri.) 16:30~17:30 |
Place |
:Dept. of Mathematics, General Research Bldg., 401 |
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Top |
Speaker |
:Tomonori Fukunaga (Kyushu Sangyo University) |
Title |
:Truncated Polyak algebras of Gauss words and
classification of Gauss words by finite type invariants. |
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(Abstract)
(PDF) |
Date |
:November 7 (Fri.) 16:30~17:30 |
Place |
:Dept. of Mathematics, General Research Bldg., 401 |
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Top |
Speaker |
:Ryoma Kobayashi (Tokyo University of Science) |
Title |
:A finite presentation of the level 2 principal congruence
subgroup of GL(n;Z) and its application |
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(Abstract)
(PDF) |
Date |
:October 10 (Fri.) 16:30~17:30 |
Place |
:Dept. of Mathematics, General Research Bldg., 401 |
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Top |
Speaker |
:Hayashi Shin (the University of Tokyo) |
Title |
:Localization of Dirac Operators on 4n+2 Dimensional Open Spin^c
Manifolds and Its Applications. |
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(Abstract)
(PDF) |
Date |
:October 3 (Fri.) 16:30~17:30 |
Place |
:Dept. of Mathematics, General Research Bldg., 401 |
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Top |
Speaker |
:Arnaud Mortier (OCAMI) |
Title |
:Cohomology of arrow diagram spaces |
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(Abstract)
(PDF) |
Date |
:July 18 (Fri.) 16:40~17:40 |
Place |
:Dept. of Mathematics, General Research Bldg., 401 |
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Top |
Speaker |
:Victoria Lebed (OCAMI) |
Title |
:Towards braid-theoretic applications of Laver tables |
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(Abstract)
(PDF) |
Date |
:July 18 (Fri.) 15:30~16:30 |
Place |
:Dept. of Mathematics, General Research Bldg., 401 |
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Top |
Speaker |
:In Dae Jong (Kinki University) |
Title |
:Annulus twist and diffeomorphic 4-manifolds II |
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(Abstract)
(PDF) |
Date |
:July 11 (Fri.) 16:30~17:30 |
Place |
:Dept. of Mathematics, General Research. Bldg., 401 |
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Top |
Speaker |
:Kouki Sato (Tokyo Gakugei University) |
Title |
:Non-orientable genus of a knot in punctured Spin 4-manifolds |
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(Abstract)
(PDF) |
Date |
:July 4 (Fri.) 16:30~17:30 |
Place |
:Dept. of Mathematics, General Research. Bldg., 401 |
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Top |
Speaker |
:Masahide Iwakiri (Saga University) |
Title |
:Unknoting numbers for handlebody-knots and Alexander quandle
colorings |
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(Abstract)
(PDF) |
Date |
:June 27 (Fri.) 16:30~17:30 |
Place |
:Dept. of Mathematics, General Research. Bldg., 401 |
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Top |
Speaker |
:Tsukasa Yashiro (Sultan Qaboos University) |
Title |
:Lower decker sets and triple points for surface-knots |
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(Abstract)
(PDF) |
Date |
:June 20 (Fri.) 16:40~17:40 |
Place |
:Dept. of Mathematics, General Research. Bldg., 401 |
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Top |
Speaker |
:Amal Al Kharusi (Sultan Qaboos University) |
Title |
:Unknotting operation and independent components of lower decker set |
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(Abstract)
(PDF) |
Date |
:June 20 (Fri.) 15:30~16:30 |
Place |
:Dept. of Mathematics, General Research. Bldg., 401 |
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Top |
Speaker |
:Daniele Zuddas (Korea Institute for Advanced Study) |
Title |
:An equivalence theorem for Lefschetz fibrations over the disk |
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(Abstract)
(PDF) |
Date |
:June 13 (Fri.) 16:30~17:30 |
Place |
:Dept. of Mathematics, General Research. Bldg., 401 |
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Top |
Speaker |
:Michihiko Fujii (Kyoto University) |
Title |
:On minimal crossing expressions of braids |
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(Abstract)
(PDF) |
Date |
:June 6 (Fri.) 16:30~17:30 |
Place |
:Dept. of Mathematics, General Research. Bldg., 401 |
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Top |
Speaker |
:Fedor Duzhin (Nanyang Technological University) |
Title |
:Brunnian braids and Brunnian links |
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(Abstract)
(PDF) |
Date |
:May 30 (Fri.) 16:30~17:30 |
Place |
:Dept. of Mathematics, General Research. Bldg., 401 |
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Top |
Speaker |
:Naoko Kamada (Nagoya City University) |
Title |
:Writhes of a twisted knot derived from weighted index diagrams |
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(Abstract)
(PDF) |
Date |
:May 16 (Fri.) 16:30~17:30 |
Place |
:Dept. of Mathematics, General Research. Bldg., 401 |
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Top |
Speaker |
:Takuya Ukida (Tokyo Institute of Technology) |
Title |
:Genus zero PALF structures on the Akbulut cork and exotic pairs |
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(Abstract)
(PDF) |
Date |
:May 9 (Fri.) 16:30~17:30 |
Place |
:Dept. of Mathematics, General Research. Bldg., 401 |
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Top |
Speaker |
:Toshifumi Tanaka (Gifu University) |
Title |
:On the maximal Thurston-Bennequin number of knots and
links in a spatial graph |
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(Abstract)
(PDF) |
Date |
:May 2 (Fri.) 16:30~17:30 |
Place |
:Dept. of Mathematics, General Research. Bldg., 401 |
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Top |
Speaker |
:Naoyuki Monden (Osaka Electro-Communication University) |
Title |
:Non-holomorphic Lefschetz fibrations with (-1)-sections |
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(Abstract)
(PDF) |
Date |
:April 25 (Fri.) 16:00~17:00 |
Place |
:Dept. of Mathematics, General Research. Bldg., 401 |
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Top |
Speaker |
:Kengo Kawamura (Osaka City University) |
Title |
:On the clasp number of a knot |
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(Abstract)
(PDF) |
Date |
:April 18 (Fri.) 16:00~17:00 |
Place |
:Dept. of Mathematics, General Research. Bldg., 401 |
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Top |
Speaker |
:Jun Ueki (Kyushu University) |
Title |
:On the universal deformations of SL(2)-representations of
2-bridge knot groups |
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(Abstract)
(PDF) |
Date |
:April 11 (Fri.) 16:00~17:00 |
Place |
:Dept. of Mathematics, General Research. Bldg., 401 |
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Top |
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Speaker: |
Akihiko Sato (Nagoya University) |
Title: |
Daikoku-Sakai-Takase move for links |
In 2012, Daikoku-Sakai-Takase constructed a move for knot diagrams whose genus doesn't increase.
In my talk, we generalize their argument to unsplittable link diagrams.
Speaker: |
Takurou Sakamoto (Nagoya University) |
Title: |
Quantum link invariant of G_2 quantum group
and the fundamental representations |
G.Kuperberg constructed the quantum link invariant that derived from G_2
quantum group and the fundamental representations. He introduced diagrams
called G_2 web that is a diagrammatization of intertwiners between tensor
representations of the fundamental representations. We refine Kuperberg's
G_2 web by introducing a new diagram and reconstruct the R-matrix from
the fundamental representations.
Speaker: |
Atsushi Ishii (Tsukuba University) |
Title: |
The Markov theorem for spatial graphs with Y-oriented IH-labeled
spatial trivalent graphs |
A spatial graph is a finite graph embedded in the 3-sphere, and a handlebody-knot
is a handlebody embedded in the 3-sphere. We introduce IH-labeled spatial
trivalent graphs, which include spatial graphs and handlebody-links. We
also introduce two kinds of orientations for them: Y-orientations and S^1
orientations. The speaker succeeded in showing the Markov theorem for IH-labeled
spatial trivalent graphs, where the two kinds of orientations work well.
In this talk, we focus on the Markov theorem for spatial graphs with Y-oriented
IH-labeled spatial trivalent graphs.
Speaker: |
Sukuse Abe (Saitama University) |
Title: |
Definition of finite type invariants of connected oriented
compact 3-manifolds |
We obtain a finite type invariant of connected oriented compact 3-manifolds.
The domain of 3-manifolds is larger than the integral homology 3-spheres
of LMO invariant. However, this invariant induces the homology of 3-manifold,
and we give a filtration to the domain of mapping class groups.
Speaker: |
Hitoshi Murakami (Tohoku University) |
Title: |
The volume conjecture and its generalizations |
I will talk about a relation of the colored Jones polynomial of a knot
to the Chern-Simons invariant, which is a kind of complex volume, and the
Reidemeister torsion associated with a representation of the knot group
to SL(2;C).
Speaker: |
Alexander Zupan (University of Texas at Austin) |
Title: |
Surface knots with small bridge number |
Recently, Gay and Kirby introduced a 4-dimensional analogue of a Heegaard
splitting called a trisection. We adapt their approach to show that every
knotted surface in the 4-sphere admits a bridge trisection; namely, there
is a decomposition of the 4-sphere into three 4-balls which splits the
surface into a collection of boundary parallel disks. This may be viewed
as the 4-dimensional version of a bridge decomposition for a knot in the
3-sphere, and as such, a bridge trisection has two complexity parameters
akin to the bridge number of a knot. We will discuss a classification of
bridge trisections with relatively low complexity. This talk is based on
joint work in progress with David Gay and Jeffrey Meier.
Speaker: |
Shumi Kinjo (Shinshu University) |
Title: |
Immersions of 3-sphere into 4-space associated with Dynkin
diagrams of types A and D |
The Smale--Hirsch h-principle implies that the group of regular homotopy
classes of immersions of m-sphere into N-space is isomorphic to the m th
homotopy group of the Stiefel manifold of m frames in N-space. The isomorphism
is given as taking the differential at each point of m-sphere and is called
the Smale invariant. In particular, Ekholm and Takase have given a formula
for the Smale invariant of an immersion of 3-sphere into 4-space by using
a singular Seifert surface for the immersion.
In this talk we will explain the construction of two infinite sequences
of immersions of the 3-sphere into 4-space, parametrized by the Dynkin
diagrams of types A and D. The construction is based on immersions of 4-manifolds
obtained as the plumbed immersions along the weighted Dynkin diagrams.
We will compute their Smale invariants by using Ekholm--Takase's formula
in terms of singular Seifert surfaces.
Speaker: |
Tomonori Fukunaga (Kyushu Sangyo University) |
Title: |
Truncated Polyak algebras of Gauss words and
classification of Gauss words by finite type invariants. |
In this talk, we study the universal finite type invariants of Gauss words
which was introduced by N. Ito and A. Gibson in [1]. In the Polyak algebra
techniques, we reduce the determination of the group structure to transformation
of a matrix into its Smith normal form and we give the simplified form
of a universal finite type invariant by means of the isomorphism of this
transformation. The advantage of this process is that we can implement
it as a computer program. We obtain the universal finite type invariant
of degree 5, 6 and 7 explicitly. Moreover, as an application, we give the
complete classification of Gauss words of rank less than or equal to 5.
This talk is based on a joint work with T. Yamaguchi (Hiroshima University)
and T. Yamanoi (Hokkaido university).
[1] N. Ito and A. Gibson, "Finite type invariants of nanowords and
nanophrases" Topol. Appl. 158 (2011), 1050 -- 1072.
Speaker: |
Ryoma Kobayashi (Tokyo University of Science) |
Title: |
A finite presentation of the level 2 principal congruence
subgroup of GL(n;Z) and its application |
Let $\Gamma_2(n)$ be the kernel of the homomorphism from $GL(n;Z)$ to $GL(n;Z/2Z)$.
Note that for an element $A$ in $\Gamma_2(n)$, the diagonal entries of
$A$ are odd, the other entries are even. A finite generating set of $\Gamma_2(n)$
has been known. In our work, we obtained a finite presentation of $\Gamma_2(n)$.
To obtain a presentation, we constructed a simply connected simplicial
complex which $\Gamma_2(n)$ acts on.
In this talk, we will introduce this complex. We note that a presentation
of $\Gamma_2(n)$ has been independently obtained also by Fullarton and
Margalit-Putman recently. As an application, we obtained a generating set
of the Torelli group of a non-orientable closed surface. We will also talk
about it.
Speaker: |
Hayashi Shin (the University of Tokyo) |
Title: |
Localization of Dirac Operators on 4n+2 Dimensional Open Spin^c
Manifolds and Its Applications. |
We observe that, on a 4n+2 dimensional Spin^c manifold which is not necessarily
closed, the symbol of the Dirac operator can be localized by a section
of its determinant line bundle to the neighborhood of its zero set. If
the zero set is compact, an integer-valued topological index of the Dirac
operator can be defined, which gives the generalization of the usual index
defined on a closed 4n+2 dimensional Spin^c manifold.
As an application of this localization method, two well known results will
be shown. One is a relation between the index and an index of a Dirac operator
of its characteristic submanifold. This formula was proved by J. Fast and
S. Ochanine for even dimensional closed Spin^c manifolds by a localization
of K-class. We prove this formula for 4n+2 dimensional Spin^c manifolds
in a different way. The other is the Riemann-Roch theorem for the Riemann
surface with boundary. We prove this formula in a topological way.
Speaker: |
Arnaud Mortier (OCAMI) |
Title: |
Cohomology of arrow diagram spaces |
Vassiliev invariants of knots are the 0-codimensional part of a theory
of "finite-type" cohomology which, apart from the level 0, is
mostly unknown. Among the computational methods at the level 0, the most
efficient may be M.Polyak and O.Viro's formulas, represented by linear
combinations of arrow diagrams. Such a combination defines an invariant
if and only if it lies in the kernel of a certain linear map, and it is
conjectured that this linear map can be enhanced into a full cochain complex,
whose i-th homology describes Vassiliev i-cocycles. In this talk, I will
show that the first step of this conjecture is true, give examples of 1-cocycles
in the space of knots, and show how to evaluate them on the two main cycles
in the space of knots, namely Gramain's and Hatcher's loops.
Speaker: |
Victoria Lebed (OCAMI) |
Title: |
Towards braid-theoretic applications of Laver tables |
Laver tables (LT) are certain finite shelves (i.e., sets endowed with a
binary operation distributive with respect to itself). They originate from
Set Theory. In spite of an elementary definition, LT have complicated combinatorial
properties. Conjecturally, they are finite approximations of the free monogenerated
shelf, whose spectacular applications to Braid Theory are well studied.
It is thus natural to expect interesting topological applications of LT
as well. This talk is devoted to our first steps in this direction. Namely,
we describe all 2- and 3-cocycles for LT, study their promisingly rich
structure, and discuss applications to Braid Theory.
Speaker: |
In Dae Jong (Kinki University) |
Title: |
Annulus twist and diffeomorphic 4-manifolds II |
We show that for any integer $n$, there exist infinitely many mutually
distinct knots such that $2$-handle additions along them with framing $n$
yield the same $4$-manifold. As a corollary, we obtain the affirmative
answer to a problem in Kirby’s list (Problem 3.6 (D)). We also explain
a relation between our result and the cabling conjecture. This is a joint
work with Tetsuya Abe.
Speaker: |
Kouki Sato (Tokyo Gakugei University) |
Title: |
Non-orientable genus of a knot in punctured Spin 4-manifolds |
For a closed 4-manifold $M$ and a knot $K$ in the boundary of punctured
$M$, we define $\gamma_M^0(K)$ to be the smallest first Betti number of
non-orientable and null-homologous surfaces in punctured $M$ with boundary
$K$. Note that $\gamma^0_{S^4}$ is equal to the non-orientable 4-ball genus
and hence $\gamma^0_M$ is generalization of the non-orientable 4-ball genus.
While it is very likely that for given $M$, $\gamma^0_M$ has no upper bound,
it is difficult to show it. In fact, even in the case of $\gamma^0_{S^4}$,
its non-boundedness was shown for the first time by Batson in 2012. In
this talk, we show that for any Spin 4-manifold $M$, $\gamma^0_M$ has no
upper bound.
Speaker: |
Masahide Iwakiri (Saga University) |
Title: |
Unknoting numbers for handlebody-knots and Alexander quandle
colorings |
A crossing change of a handlebody-knot is that of a spatial graph representing
it. We see that any handlebody-knot can be deformed into trivial one by
some crossing changes. So we define the unknotting numbers for handlebody-knots.
In the case classical knots, which are considered as genus one handlebody-knots,
Clark, Elhamdadi, Saito and Yeatman gave lower bounds of the Nakanishi
indices by the numbers of some finite Alexander quandle colorings, and
hence they also gave lower bounds of the unknotting numbers. In this talk,
we give lower bounds of the unknotting numbers for handlebody-knots with
any genus by the numbers of some finite Alexander quandle colorings of
type at most 3.
Speaker: |
Tsukasa Yashiro (Sultan Qaboos University) |
Title: |
Lower decker sets and triple points for surface-knots |
A surface-knot is a closed oriented surface embedded in 4-space. A surface
diagram of a surface-knot is the projected image in 3-space under the orthogonal
projection with crossing information. The pre-image of multiple point sets
of a surface diagram is called a double decker set that is the union of
lower and upper decker sets. A crossing point in a lower decker set corresponds
to a triple point in the diagram. If a diagram is coloured by a quandle,
we can define degenerate triple points. In this talk we estimate the number
of non-degenerate triple points in a coloured diagram corresponding to
a connected component of the lower decker set.
Speaker: |
Amal Al Kharusi (Sultan Qaboos University) |
Title: |
Unknotting operation and independent components of lower decker set |
This talk is divided into two main parts. In the first part, a generalization
of the notion of crossing change operation of knot diagrams to surface-knot
diagrams will be discussed. The second part involves a method for detecting
prime surface-knots by using the colourings. In addition, the notion of
independent components of lower decker set will be demonstrated.
Speaker: |
Daniele Zuddas (Korea Institute for Advanced Study) |
Title: |
An equivalence theorem for Lefschetz fibrations over the disk |
In this talk we present the moves for (achiral) Lefschetz fibrations over
the disk, that give a complete interpretation of Kirby calculus for 4-manifolds
in the setting of Lefschetz fibrations.
We discuss also an application to open book decompositions of 3-manifolds.
Speaker: |
Michihiko Fujii (Kyoto University) |
Title: |
On minimal crossing expressions of braids |
First, we give a usual projection of braid onto the two dimensional Euclidean
space.
Then we consider the problem how a minimal crossing braid is obtained from
the projection.
Speaker: |
Fedor Duzhin (Nanyang Technological University) |
Title: |
Brunnian braids and Brunnian links |
A Brunnian link is a link that becomes trivial after removing any of its
components. Similarly, a Brunnian braid is a braid that becomes trivial
after removing any of its strands. According to Alexander's theorem, any
link can be obtained as a closure of some braid. Obviously, the closure
of a Brunnian braid is a Brunnian link. However, some not every Brunnian
link is the closure of a Brunnian braid. In this talks we'll discuss some
ways of constructing Brunnian links that cannot be obtained as a closure
of a Brunnian braid.
Speaker: |
Naoko Kamada (Nagoya City University) |
Title: |
Writhes of a twisted knot derived from weighted index diagrams |
The odd writhe is a numerical invariant of a virtual knot which is defined
by L. Kauffman. Y. Im, K. Lee and Y. Lee and A. Henrich introduced a polynomial
invariant of a virtual knot, called the index polynomial. S. Satoh and
K. Taniguchi introduced a series of numerical invariants of a virtual knot,
called n-writhes, which induce the odd writhe and are related with the
index polynomial. In this talk, we discuss a generalization of them to
a twisted knot by use of weighted index diagrams.
Speaker: |
Takuya Ukida (Tokyo Institute of Technology) |
Title: |
Genus zero PALF structures on the Akbulut cork and exotic pairs |
Loi and Piergallini proved that every compact Stein surface admits a PALF
(positive allowable Lefschetz fibration over a 2-disk with bounded fibers).
Akbulut and Yasui introduced cork twist to construct various families of
arbitrary many compact Stein surfaces which are mutually homeomorphic but
not diffeomorphic (i.e. exotic pairs). In this talk, we construct genus
zero PALF on the Akbulut cork and exotic pairs.
Speaker: |
Toshifumi Tanaka (Gifu University) |
Title: |
On the maximal Thurston-Bennequin number of knots and
links in a spatial graph |
A spatial graph is said to be mTB-realizable if it is ambient isotopic
to a Legendrian graph such that all its cycles realize their maximal Thurston-Bennequin
numbers. In this talk, I will give an example of an infinite family of
spatial embeddings of the complete graph on 4 vertices that are mTB-realizable
and show that if a spatial graph contains a completely splittable link
as the union of all its cycles, then it is mTB-realizable. I will also
show that if a finite graph G contains two cycles that have no common edges
and vertices, then there is a spatial embedding of G such that it is not
mTB-realizable.
Speaker: |
Naoyuki Monden (Osaka Electro-Communication University) |
Title: |
Non-holomorphic Lefschetz fibrations with (-1)-sections |
The notion of Lefschetz fibrations in two-dimentional complex geometry
(i.e., holomorphic Lefschetz fibrations) was generalized by Moishezon to
four-dimensional topology. It is then natural to ask how far Lefschetz
fibrations in four-dimensional topology are from holomorphic ones. To answer
this question, various kinds of examples of non-holomorphic Lefschetz fibrations
have been constructed. In particular, from Donaldson's theorem, it follows
that there are infinitely many non-holomorphic Lefschetz fibrations with
(-1)-sections. In this talk, we construct explicit examples of non-holomorphic
Lefschetz fibrations with (-1)-sections without Donaldson's theorem. This
is a joint work with Noriyuki Hamada (The university of Tokyo) and Ryoma
Kobayashi (Tokyo university of science).
Speaker: |
Kengo Kawamura (Osaka City University) |
Title: |
On the clasp number of a knot |
Every knot in $S^{3}$ bounds a singular disk in $S^{3}$ whose singular
set consists of only clasp singularities. The clasp number $c(K)$ of a
knot $K$ is the minimal number of clasp singularities among all such singular
disks bounded by $K$. In this talk, we determine the clasp number of a
certain knot by using a characterization of the Alexander module, and we
investigate the clasp numbers of $2$-bridge knots.
This is a joint work with T. Kadokami.
Speaker: |
Jun Ueki (Kyushu University) |
Title: |
On the universal deformations of SL(2)-representations of
2-bridge knot groups |
Joint work with M. Morishita, Y. Takakura and Y. Terashima.
In this talk, we first review Alexander-Fox theory and Iwasawa theory as
the moduli theories of 1-dim. representations of knot/prime groups $G$.
Then, we study the analogue story of prime groups, Hida-Mazur’s theory
of 2-dim. representations, for knot groups:
(1) we overview the deformation theory of SL(2)-representation,
(2) state the relation between character variety and universal deformation
ring, and
(3) construct the universal deformation of Riley's standard SL(2)-representation
of 2-bridge knot group.
It should be remarked that In the dictionary of analogy in Arithmetic Topology,
knots correspond to primes, and GL(2) Alexander polynomials $A(r,s)$ correspond
to $p$-adic L-functions $L(r,s)$, where the parameters $s$ and $r$ come
from GL(1) and SL(2) theories respectively.
Last Modified on February 20, 2015.
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