Organizer: Masahide Iwakiri
| Date | February 12 (Fri.) 16：30～17：30 |
| Speaker | Mark Powell（University of Edinburgh） |
| Title | Knot Concordance and Twisted Blanchfield Forms |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | February 5 (Fri.) 16：00～17：00 |
| Speaker | Kokoro Tanaka (Tokyo Gakugei University) |
| Title | A recent approach to the smooth 4-dimensional Poincare conjecture |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | January 15 (Fri.) 16：00～17：00 |
| Speaker | Zhang Mingxing (Osaka City University) |
| Title | Standard surfaces embedded in a genus 2 handlebody |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | January 8 (Fri.) 16：00～17：00 |
| Speaker | Teruhisa Kadokami (Dalian University of Technology) |
| Title | Alexander polynomials of algebraically split amphicheiral links (partially joint work with Akio Kawauchi) |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | December 4 (Fri.) 16：00～17：00 |
| Speaker | Saki Umeda (Nara Women's University) |
| Title | On topological methods for constructing efficient mixings |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | November 27 (Fri.) 16：00～17：00 |
| Speaker | Taizo Kanenobu (Osaka City University) |
| Title | $H(2)$-Gordian Distance of Knots |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | November 20 (Fri.) 16：00～17：00 |
| Speaker | Kouichi Yasui (RIMS, Kyoto University) |
| Title | On corks of 4-manifolds (joint work with Selman Akbulut) |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | November 6 (Fri.) 16：00～17：00 |
| Speaker | Hiromasa Moriuchi（OCAMI） |
| Title | An enumeration of non-prime theta-curves and handcuff graphs with up to seven crossings |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | October 30 (Fri.) 16：00～17：00 |
| Speaker | Kanako Oshiro (Hiroshima University) |
| Title | Cocycle invariants with quandles and symmetric doubles for oriented links |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | October 23 (Fri.) 16：00～17：00 |
| Speaker | Ryo Hanaki (Waseda University) |
| Title | On intrinsically knotted or completely 3-linked graphs (joint work with Ryo Nikkuni, Kouki Taniyama and Akiko Yamazaki) |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | October 9 (Fri.) 16：00～17：00 |
| Speaker | Yuichi Kabaya（OCAMI） |
| Title | A complex volume formula via quandle shadow coloring (joint work with Ayumu Inoue) |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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). |
| Date | October 2 (Fri.) 16：00～17：00 |
| Speaker | Masahide Iwakiri（OCAMI） |
| Title | Surface-links represented by 4-charts and quandle cocycle invariants |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | July 24 (Fri.) 16：00～17：00 |
| Speaker | Sakie Suzuki (RIMS, Kyoto University) |
| Title | On the universal $sl_2$ invariant of ribbon bottom tangles |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | July 17 (Fri.) 16：00～17：00 |
| Speaker | Yeonhee Jang (Hiroshima University) |
| Title | Algebraic links with 3-bridge presentations |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | July 3 (Fri.) 16：00～17：00 |
| Speaker | Motoo Tange (RIMS, Kyoto University) |
| Title | Branched covering description of lens space surgery |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | June 26 (Fri.) 16：10～17：10 |
| Speaker | Yoshiro Yaguchi (Hiroshima University) |
| Title | Determining the Hurwitz orbit of any tuple of the standard generators of the braid group |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | June 26 (Fri.) 16：00～17：00 |
| Speaker | Tsukasa Yashiro (Sultan Qaboos University) |
| Title | On annulus twist tracks |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | June 19 (Fri.) 16：00～17：00 |
| Speaker | Ryo Nikkuni（Tokyo Woman's Christian University） |
| Title | A refinement of Conway-Gordon's theorem |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | June 12 (Fri.) 16：00～17：00 |
| Speaker | Takahito Kuriya (RIMS, Kyoto University) |
| Title | Tame knot theory and knot mosaic theory are equivalent |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | June 5 (Fri.) 16：10～17：10 |
| Speaker | Iain Aitchison（University of Melbourne） |
| Title | Explicit moduli for closed genus 2 surfaces (joint work with Armando Rodado) |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | June 5 (Fri.) 15：00～16：00 |
| Speaker | Takefumi Nosaka (RIMS, Kyoto University) |
| Title | Quandles and $C^{\infty}$-manifolds |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | May 29 (Fri.) 16：10～17：10 |
| Speaker | Masaki Tsukamoto (Kyoto University) |
| Title | Asymptotic distribution of critical values (joint work with Tomohiro Fukaya) |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | May 29 (Fri.) 15：00～16：00 |
| Speaker | Kumi Kobata（OCAMI） |
| Title | Knots contained in spatial embeddings of complete graphs and circular embeddings of knots (joint work with Toshifumi Tanaka) |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | May 15 (Fri.) 16：00～17：00 |
| Speaker | Kengo Kishimoto (Graduate School of Science, Osaka City University) |
| Title | The IH-complex of spatial trivalent graphs (joint work with Atsushi Ishii) |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | May 8 (Fri.) 14：00～15：00 |
| Speaker | Tetsuya Abe (Graduate School of Science, Osaka City University, JSPS Research Fellow) |
| Title | The band-unknotting number of a knot (joint work with Ryuji Higa) |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | April 24 (Fri.) 14：00～15：00 |
| Speaker | Daniel Moskovich（Research Institute for Mathematical Sciences, Kyoto University) |
| Title | Equivalence relations generated by surgeries which preserve metabelian information |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | April 17 (Fri.) 16：00～17：00 |
| Speaker | In Dae JONG (Graduate School of Science, Osaka City University) |
| Title | On a simplicial complex of the Alexander polynomials |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
| Date | April 10 (Fri.) 16：00～17：00 |
| Speaker | Tatsuya Tsukamoto (Osaka Institute of Technology) |
| Title | Delta-cobordism of certain satellite links (joint work with Tetsuo Shibuya and Akira Yasuhara) |
| Place | Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract | 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. |
