講 演 者 |
:Mark Powell (University of Edinburgh) |
タ イ ト ル |
:Knot Concordance and Twisted Blanchfield Forms |
|
(アブストラクト)
(PDF) |
日 時 |
:2月12日(金)16:30~17:30 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:田中心(東京学芸大学) |
タ イ ト ル |
:A recent approach to the smooth 4-dimensional Poincare conjecture |
|
(アブストラクト)
(PDF) |
日 時 |
:2月5日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:張明星(大阪市立大学) |
タ イ ト ル |
:Standard surfaces embedded in a genus 2 handlebody |
|
(アブストラクト)
(PDF) |
日 時 |
:1月15日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:門上晃久(大連理工大学) |
タ イ ト ル |
:Alexander polynomials of algebraically split amphicheiral links
(partially joint work with Akio Kawauchi) |
|
(アブストラクト)
(PDF) |
日 時 |
:1月8日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:梅田早希(奈良女子大学) |
タ イ ト ル |
:On topological methods for constructing efficient mixings |
|
(アブストラクト)
(PDF) |
日 時 |
:12月4日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:金信泰造(大阪市立大学) |
タ イ ト ル |
:$H(2)$-Gordian Distance of Knots |
|
(アブストラクト)
(PDF) |
日 時 |
:11月27日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:安井弘一(京都大学数理解析研究所(RIMS)) |
タ イ ト ル |
:On corks of 4-manifolds
(joint work with Selman Akbulut) |
|
(アブストラクト)
(PDF) |
日 時 |
:11月20日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:森内博正 (大阪市立大学数学研究所(OCAMI)) |
タ イ ト ル |
:An enumeration of non-prime theta-curves and handcuff graphs
with up to seven crossings |
|
(アブストラクト)
(PDF) |
日 時 |
:11月6日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:大城佳奈子(広島大学大学院理学研究科) |
タ イ ト ル |
:Cocycle invariants with quandles and symmetric doubles for oriented links |
|
(アブストラクト)
(PDF) |
日 時 |
:10月30日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:花木良 (早稲田大学大学院教育学研究科) |
タ イ ト ル |
:On intrinsically knotted or completely 3-linked graphs
(joint work with Ryo Nikkuni, Kouki Taniyama and Akiko Yamazaki) |
|
(アブストラクト)
(PDF) |
日 時 |
:10月23日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:蒲谷祐一 (大阪市立大学数学研究所(OCAMI)) |
タ イ ト ル |
:A complex volume formula via quandle shadow coloring
(joint work with Ayumu Inoue) |
|
(アブストラクト)
(PDF) |
日 時 |
:10月9日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:岩切雅英 (大阪市立大学数学研究所(OCAMI)) |
タ イ ト ル |
:Surface-links represented by 4-charts and quandle cocycle invariants |
|
(アブストラクト)
(PDF) |
日 時 |
:10月2日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:鈴木咲衣 (京都大学数理解析研究所) |
タ イ ト ル |
:On the universal $sl_2$ invariant of ribbon bottom tangles |
|
(アブストラクト)
(PDF) |
日 時 |
:7月24日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:張 娟姫 (広島大学) |
タ イ ト ル |
:Algebraic links with 3-bridge presentations |
|
(アブストラクト)
(PDF) |
日 時 |
:7月17日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:丹下基生 (京都大学数理解析研究所) |
タ イ ト ル |
:Branched covering description of lens space surgery |
|
(アブストラクト)
(PDF) |
日 時 |
:7月3日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:矢口義朗 (広島大学) |
タ イ ト ル |
:Determining the Hurwitz orbit of any tuple of the standard
generators of the braid group |
|
(アブストラクト)
(PDF) |
日 時 |
:6月26日(金)16:10~17:10 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:屋代司(サルタンカブース大学) |
タ イ ト ル |
:On annulus twist tracks |
|
(アブストラクト)
(PDF) |
日 時 |
:6月26日(金)15:00~16:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:新國 亮(東京女子大学) |
タ イ ト ル |
:A refinement of Conway-Gordon's theorem |
|
(アブストラクト)
(PDF) |
日 時 |
:6月19日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:栗屋隆仁 (京都大学数理解析研究所) |
タ イ ト ル |
:Tame knot theory and knot mosaic theory are equivalent |
|
(アブストラクト)
(PDF) |
日 時 |
:6月12日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:Iain Aitchison (University of Melbourne) |
タ イ ト ル |
:Explicit moduli for closed genus 2 surfaces
(joint work with Armando Rodado) |
|
(アブストラクト)
(PDF) |
日 時 |
:6月5日(金)16:10~17:10 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:野坂武史 (京都大学数理解析研究所) |
タ イ ト ル |
:Quandles and $C^{\infty}$-manifolds |
|
(アブストラクト)
(PDF) |
日 時 |
:6月5日(金)15:00~16:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:塚本真輝(京都大学大学院理学研究科) |
タ イ ト ル |
:Asymptotic distribution of critical values
(joint work with Tomohiro Fukaya) |
|
(アブストラクト)
(PDF) |
日 時 |
:5月29日(金)16:10~17:10 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:小畑久美 (大阪市立大学数学研究所(OCAMI)) |
タ イ ト ル |
:Knots contained in spatial embeddings of complete graphs and
circular embeddings of knots
(joint work with Toshifumi Tanaka) |
|
(アブストラクト)
(PDF) |
日 時 |
:5月29日(金)15:00~16:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:岸本健吾(大阪市立大学大学院理学研究科) |
タ イ ト ル |
:The IH-complex of spatial trivalent graphs
(joint work with Atsushi Ishii) |
|
(アブストラクト)
(PDF) |
日 時 |
:5月15日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:安部哲哉
(大阪市立大学大学院理学研究科, 日本学術振興会特別研究員(DC2)) |
タ イ ト ル |
:The band-unknotting number of a knot
(joint work with Ryuji Higa) |
|
(アブストラクト)
(PDF) |
日 時 |
:5月8日(金)14:00~15:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:Daniel Moskovich(京都大学数理解析研究所) |
タ イ ト ル |
:Equivalence relations generated by surgeries
which preserve metabelian information |
|
(アブストラクト)
(PDF) |
日 時 |
:4月24日(金)14:00~15:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:鄭 仁大 (大阪市立大学大学院理学研究科) |
タ イ ト ル |
:On a simplicial complex of the Alexander polynomials |
|
(アブストラクト)
(PDF) |
日 時 |
:4月17日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
講 演 者 |
:塚本達也(大阪工業大学) |
タ イ ト ル |
:Delta-cobordism of certain satellite links
(joint work with Tetsuo Shibuya and Akira Yasuhara) |
|
(アブストラクト)
(PDF) |
日 時 |
:4月10日(金)16:00~17:00 |
場 所 |
:数学 第3セミナー室(3153) |
|
Top |
|
|
講 演 者: |
Mark Powell (University of Edinburgh) |
タ イ ト ル: |
Knot Concordance and Twisted Blanchfield Forms |
In this talk I will recall the notion of knot concordance as defined by
Fox and Milnor, which asks whether a knot in S3 bounds a disk in 4 space
D4. The work of Casson and Gordon involved a two stage obstruction theory
which depends on the intersection form of a 4-manifold. This has been generalised
by the work of Cochran-Orr-Teichner.
I shall discuss an obstruction theory which is intrinsically 3-dimensional,
using Blanchfield linking forms with coefficients twisted using metabelian
representations of the knot group. These linking forms obstruct null-concordance.
We then describe an algorithm to construct the symmetric chain complex
of the universal cover of a knot exterior, and then use this to make calculations
of the twisted Blanchfield forms.
講 演 者: |
田中心(東京学芸大学) |
タ イ ト ル: |
A recent approach to the smooth 4-dimensional Poincare conjecture |
We will report on the preprint (arXiv:0906.5177) written by M. Freedman,
R. Gompf, S. Morrison and K. Walker. They proposed some strategies to disprove/prove
the smooth 4-dimensional Poincare conjecture, which is called "SPC4"
for short. In this talk, we mainly focus on one of their strategies to
disprove SPC4 by using the Rasmussen invariant, which is a knot concordance
invariant derived from (a variant of) the Khovanov homology theory.
講 演 者: |
張明星(大阪市立大学) |
タ イ ト ル: |
Standard surfaces embedded in a genus 2 handlebody |
In this talk, we will introduce some disks and annuli in a genus 2 handle
body, which we call them standard. And the standard surfaces will help
us know the incompressible surfaces in a knot complement.
講 演 者: |
門上晃久(大連理工大学) |
タ イ ト ル: |
Alexander polynomials of algebraically split amphicheiral links
(partially joint work with Akio Kawauchi) |
We provide necessary conditions for algebraically split links to be amphicheiral
by the Alexander polynomials of them.
Firstly, we study algebraically split amphicheiral links only by using
the Alexander polynomials.
Secondly (this part is the joint work), we study them by using the signature
invariants.
講 演 者: |
梅田早希(奈良女子大学) |
タ イ ト ル: |
On topological methods for constructing efficient mixings |
Topological nature of stirring fluid by using finitely many rods is closely
related to Nielsen-Thurston theory and braid theory. It is natural to expect
that stirrings corresponding to pseudo-Anosov braids can mix up fluid efficiently.
Making use of this idea, various mixing devices are proposed by several
authors, and their efficiencies are confirmed by using computer simulations
and experiments. In this talk, we introduce other mixing device with simple
structures consisting of few gears, where the movements of the rods are
hypotrochoid curves. We show that the braid corresponding to the movement
is pseudo-Anosov type by using linking numbers of the closure of it and
covering space. We believe that our device has an advantage for practical
use from the viewpoint of the efficiency of the mixings.
講 演 者: |
金信泰造(大阪市立大学) |
タ イ ト ル: |
$H(2)$-Gordian Distance of Knots |
An $H(2)$-move is a local move of a knot, which is performed by adding
a half-twisted band. It is known an $H(2)$-move is an unknotting operation.
We define the $H(2)$-{Gordian distance} of two knots to be the minimum
number of $H(2)$-moves needed to transform one into the other. We give
several methods to estimate the $H(2)$-Gordian distance of knots; many
of them are generalizations of the methods used to estimate an $H(2)$-unknotting
number. Then we give a table of $H(2)$-Gordian distances of knots with
up to $7$ crossings.
講 演 者: |
安井弘一(京都大学数理解析研究所(RIMS)) |
タ イ ト ル: |
On corks of 4-manifolds
(joint work with Selman Akbulut) |
It is known that every exotic smooth structure on a simply connected closed
4-manifold is determined by a codimention zero compact contractible submanifold
and an involution on the boundary. Such a pair is called a cork. In this
talk, we give various examples of cork structures of 4-manifolds.
講 演 者: |
森内博正 (大阪市立大学数学研究所(OCAMI)) |
タ イ ト ル: |
An enumeration of non-prime theta-curves and handcuff graphs
with up to seven crossings |
We have enumerated all the prime theta-curves and handcuff graphs with
up to seven crossings before. We can composite many spatial graphs by using
``connected sum'' of them. However, for spatial graphs, ``connected sum''
is not unique. In this talk, we enumerate non-prime theta-curves and handcuff
graphs with up to seven crossings by using algebraic tangles and non-prime
basic theta-polyhedra.
講 演 者: |
大城佳奈子(広島大学大学院理学研究科) |
タ イ ト ル: |
Cocycle invariants with quandles and symmetric doubles for oriented links |
Quandle cocycle invariants are introduced for oriented (classical or surface)
links and they are usefully applied for several studies of classical links
and orientable surface-links. On the other hand, symmetric quandle cocycle
invariants were introduced as a quandle invariant for all classical links
and surface-links. However, by the construction of symmetric quandle homology
groups and knot invariants, it is expected that the symmetric quandle invariants
are weaker than the quandle invariants for oriented links.
Is it ture? In this talk, we give the answer.
講 演 者: |
花木良 (早稲田大学大学院教育学研究科) |
タ イ ト ル: |
On intrinsically knotted or completely 3-linked graphs
(joint work with Ryo Nikkuni, Kouki Taniyama and Akiko Yamazaki) |
It is known that the graphs obtained from $K_7$ by Delta-Y moves are intrinsically
knotted.
Flapan and Naimi showed that there exists a graph obtained from $K_7$ by
Delta-Y moves and Y-Delta moves which is not intrinsically knotted.
We show that the graphs obtained from $K_7$ by Delta-Y moves and Y-Delta
moves are intrinsically knotted or completely 3-linked.
Here a graph is said to be intrinsically knotted or completely 3-linked
if every embedding of the graph in $R3$ contains a nontrivial knot or a
3-component link each of whose 2-component sublink is nonsplittable.
講 演 者: |
蒲谷祐一 (大阪市立大学数学研究所(OCAMI)) |
タ イ ト ル: |
A complex volume formula via quandle shadow coloring
(joint work with Ayumu Inoue) |
For a hyperbolic manifold M, Vol(M) + i CS(M) is called the complex volume
of M where Vol(M) and CS(M) are volume and Chern-Simons invariant of M
respectively.
W. Neumann defined the extended Bloch group \hat{B}(C) and gave a formula
of the complex volume using \hat{B}(C).
In this talk, we introduce a construction of the element of extended Bloch
group from the quandle 2-cycle associated with a shadow coloring. Combined
with works of Neumann and Dupont-Zickert, we obtain a formula of complex
volume.
This is a joint work with Ayumu Inoue (Tokyo Institute of Technology) .
講 演 者: |
岩切雅英 (大阪市立大学数学研究所(OCAMI)) |
タ イ ト ル: |
Surface-links represented by 4-charts and quandle cocycle invariants |
Any surface-link can be deformed into the closure of a surface braid of some degree $m$
and can be also represented by an $m$-chart. In this talk, we will study the surface-links
represented by $4$-charts and their quandle cocycle invariant, and show the result
related to the $w$-index of surface links.
講 演 者: |
鈴木咲衣 (京都大学数理解析研究所) |
タ イ ト ル: |
On the universal $sl_2$ invariant of ribbon bottom tangles |
A bottom tangle is a tangle in a cube consisting of arc components whose
boundary points are on a line in the bottom square of the cube. A ribbon
bottom tangle is a bottom tangle whose closure is a ribbon link. For every
$n$-component ribbon bottom tangle $T$, we prove that the universal invariant
of $T$ associated to the quantized enveloping algebra $U_h(sl_2)$ is contained
in a certain subalgebra of the $n$-fold completed tensor power of $U_h(sl_2)$.
This result is applied to the colored Jones polynomial of ribbon links.
講 演 者: |
張 娟姫 (広島大学) |
タ イ ト ル: |
Algebraic links with 3-bridge presentations |
An algebraic link is a link in the three sphere whose double branched covering
is a graph manifold. In this talk, we give a classification of 3-bridge
algebraic links and their 3-bridge presentations up to isotopy. We use
genus-2 Heegaard splittings of graph manifolds to classify them. In particular,
we focus on the relation between 3-bridge presentations for links and genus-2
Heegaard splittings of 3-manifolds, and show with an example how to distinguish
two 3-bridge spheres up to isotopy.
講 演 者: |
丹下基生 (京都大学数理解析研究所) |
タ イ ト ル: |
Branched covering description of lens space surgery |
The speaker has studied knots in Poincare homology sphere yielding lens
spaces by Dehn surgery. From the fact that the examples are strongly invertible,
we concretely describe the Dehn surgeries. As a corollary we show that
a class of Brieskorn homology spheres and the splicing of them give rise
to lens spaces by Dehn surgery.
講 演 者: |
矢口義朗 (広島大学) |
タ イ ト ル: |
Determining the Hurwitz orbit of any tuple of the standard
generators of the braid group |
Hurwitz action of the $n$-braid group $B_n$ on the $n$-fold direct product
${B_m}^n$ of the $m$-braid group $B_m$ is studied. We determine the orbit
of any $n$-tuple of the $n$ distinct standard generators of $B_{n+1}$.
In addition, we show that any $n$-tuple of the $n$ distinct standard generators
of $B_{n+1}$ is transformed into any of those by Hurwitz action together
with the action of $B_{n+1}$ by conjugation.
講 演 者: |
屋代司(サルタンカブース大学) |
タ イ ト ル: |
On annulus twist tracks |
A generic surface in $3$-space can be deformed into another generic surface
by a finite sequence of local moves. Some of these sequence can be viewed
as projected images of isotopy deformations of a surface embedded in $4$-space.
We call such a sequence liftable. In this talk we will discuss about special
regular homotopy deformations on an annulus called annulus twist track.
We give a necessary and sufficient condition for an annulus twist track
to be liftable.
講 演 者: |
新國 亮(東京女子大学) |
タ イ ト ル: |
A refinement of Conway-Gordon's theorem |
In 1983, Conway and Gordon showed that for every spatial complete graph
on 6 vertices, the sum of linking numbers over all of the constituent 2-component
links is congruent to 1 modulo 2, and for every spatial complete graph
on 7 vertices, the sum of Arf invariants over all of Hamiltonian knots
is also congruent to 1 modulo 2. In this talk, we give an integral lift
of Conway-Gordon's theorem and its applications.
講 演 者: |
栗屋隆仁 (京都大学数理解析研究所) |
タ イ ト ル: |
Tame knot theory and knot mosaic theory are equivalent |
J. Lomonaco Jr and Louis H. Kauffman conjectured that tame knot theory
and knot mosaic theory are equivalent. We give a proof of the Lomonaco-Kauffman
conjecture.
講 演 者: |
Iain Aitchison (University of Melbourne) |
タ イ ト ル: |
Explicit moduli for closed genus 2 surfaces
(joint work with Armando Rodado) |
We explicitly describe the Teichmuller and Moduli spaces for closed surfaces
of genus 2, following the path suggested by Rivin, Leibon and Springborn:
(Compactified) Teichmuller space is tiled by copies of 10 explicit 6-dimensional
polyhedra, each parametrizing the possible realizations in hyperbolic geometry
of a Delauney triangulation/circle pattern with one of 10 specified underlying
graphs.
Coordinates for the polyhedra allow the surface to be explicitly reconstructed
as a hyperbolic surface. Symmetries of the polyhedra can be explicitly
described, thereby giving the corresponding decomposition of moduli space.
This answers, in the genus 2 case, questions raised by Sullivan and Witten
in recent years: that Weierstrass points may help to describe moduli for
closed surfaces, and that there may be a cell decomposition with natural
compactification for closed surfaces of genus 2 or more.
This is the first explicit cell decomposition of the (compactified) moduli
space of any closed hyperbolic surface.
The approach uses the fixed points of the unique hyperelliptic involution
on genus 2 surfaces, which is an isometry with respect to any hyperbolic
structure, and had been suggested by Aitchison at Xi'an in 2002. Rodado
completed his PhD at Melbourne, implementing this approach using linear
programming underlying circle patterns, and finding all candidate graphs
describing generic Delaunay circle patterns.
We thus describe Rodado's work, and subsequent joint work explicitly describing
the 10 6-dimensional polytopes of the natural compactification of Teichmuller
and Moduli space.
講 演 者: |
野坂武史 (京都大学数理解析研究所) |
タ イ ト ル: |
Quandles and $C^{\infty}$-manifolds |
There are many studies for finite quandles.
This talk explores manifolds $X$ with a quandle structure and presents some examples and properties of $X$.
I show that $X$ is a homogenous space ($X=G/H$) under a natural condition.
Moreover, with defining a quandle measure of $X$, I arrive at some results
as analogous to cases of finite quandles.
講 演 者: |
塚本真輝(京都大学大学院理学研究科) |
タ イ ト ル: |
Asymptotic distribution of critical values
(joint work with Tomohiro Fukaya) |
Let $X$ be a closed manifold and $f:X\times X\to \mathbb{R}$ be a smooth
function.
Define $f_n:X^{n+1}\to \mathbb{R}$ by $f_n(x_1, \cdots, x_{n+1}) := \sum
f(x_i, x_{i+1})/n$.
We study the asymptotic distribution of the critical values of $f_n$ as
$n$ goes to infinity.
This is the joint work with Tomohiro Fukaya.
講 演 者: |
小畑久美 (大阪市立大学数学研究所(OCAMI)) |
タ イ ト ル: |
Knots contained in spatial embeddings of complete graphs and
circular embeddings of knots
(joint work with Toshifumi Tanaka) |
This is a joint work with Toshifumi Tanaka.
We construct a linear spatial embedding of the complete graph on 2n-1 (or
2n) vertices which contains the torus knot of type (2n-5, 2) (n is greater
than or equal to 4). And we define the circular number of a knot. We show
that a knot has the circular number 3 if and only if the knot is a trefoil
knot, and the figure-eight knot has the circular number 4.
講 演 者: |
岸本健吾(大阪市立大学大学院理学研究科) |
タ イ ト ル: |
The IH-complex of spatial trivalent graphs
(joint work with Atsushi Ishii) |
This is a joint work with Atsushi Ishii.
An IH-move is a local spatial move of a spatial trivalent graph.
We define the IH-distance between two spatial trivalent graphs by the minimal
number of IH-moves needed to transform one into the other.
We give a lower bound for the IH-distance by using invariants for flowed
spatial graphs.
We introduce the IH-complex and show some fundamental properties of the
complex.
講 演 者: |
安部哲哉
(大阪市立大学大学院理学研究科, 日本学術振興会特別研究員(DC2)) |
タ イ ト ル: |
The band-unknotting number of a knot
(joint work with Ryuji Higa) |
This is a joint work with Ryuji Higa. A band-move is a local move of a
link diagram which is performed by adding a band. We define the band-unknotting
number of a knot K to be the minimum number of band-moves needed to transform
a diagram of K into that of the trivial knot. Note that, in the definition
of the band-unknotting number of a knot K, we may use Reidemeister moves
after applying a band-move and the sequence from a diagram of K to that
of the trivial knot may contain a diagram of a link.
In this talk, we show that the band-unknotting number of a knot K is less
than or equal to half the crossing number of K and the equality holds if
and only if K is the trivial knot or the figure-eight knot.
To prove this, we give a characterization of the figure-eight knot.
講 演 者: |
Daniel Moskovich(京都大学数理解析研究所) |
タ イ ト ル: |
Equivalence relations generated by surgeries
which preserve metabelian information |
We consider knots modulo surgery which preserved metabelian subgroups of
the knot group. When these subgroups are fixed and finite, the number of
equivalence classes is finite. For certain groups the equivalence classes
can be completely determined. Universally, the maximal metabelian subgroup
of a knot is preserved by surgeries along unit-framed links which form
boundary links with the knot. The induced equivalence relation interpolates
between loop Y_1-equivalence (S-equivalence) and loop Y_2-equivalence.
講 演 者: |
鄭 仁大 (大阪市立大学大学院理学研究科) |
タ イ ト ル: |
On a simplicial complex of the Alexander polynomials |
We detect whether a reciprocal integer polynomial $f(t)=\sum_{i=1}4 a_i
t^i$ with $|a_0| \le 100$ is realized as the Alexander polynomial of an
alternating knot.
In addition, we introduce a simplicial complex structure on the set of
the Alexander polynomials and study a subcomplex consists of the Alexander
polynomials of alternating knots.
講 演 者: |
塚本達也(大阪工業大学) |
タ イ ト ル: |
Delta-cobordism of certain satellite links
(joint work with Tetsuo Shibuya and Akira Yasuhara) |
This is a joint work with Tetsuo Shibuya and Akira Yasuhara.
Delta-cobordism is the equivalence relation generated by cobordism and
self delta-moves.
We study a relation between delta-cobordism of certain satellite links
and delta-cobordism of their cores.
最終更新日: 2010年2月5日
(C)大阪市大数学教室
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