International Workshop on Low-dimensional Topology
Date: May 6-7, 2016
Place: DUT International Conference Center, Dalian, China
Host: School of Mathematical Sciences, Dalian University of Technology
Co-Host: School of Mathematics, Liaoning Normal University
Invited Speakers:
Prof. Yukio Matsumoto, Gakushuin University, Japan
Prof. Akio Kawauchi, Osaka City University, Japan
Prof. Mikio Furuta, University of Tokyo, Japan
Prof. Seiichi Kamada, Osaka City University, Japan
Prof. Kazuo Habiro, Kyoto University, Japan
Prof. Ki Hyoung Ko, KAIST, Korea
Prof. Gyo Taek Jin, KAIST, Korea
Prof. SONg Yongjin, Inha Univeristy, Korea
Prof. Andrei Yurievich Vesnin, Sobolev Institute of Mathematics, Russia
Prof. Velariy Bardakov, Novosibirsk State University, Russia
Prof. FANG Fuquan, Capital Normal University, China
Prof. ZHAO Xuezhi, Capital Normal University, China
Prof. QIU Ruifeng, East China Normal University, China
Prof. YANG Zhiqing, Dalian University of Technology, China
Prof. JIN Xianan, Xiamen University, China
Organizing Committee:
WU Jie, National University of Singapore
LIU Ximin, Dalian University of Technology
LEI Fengchun, Dalian University of Technology
Contact: Ms. LI Fengling, email: dutlfl@163.com
Homepage: http://math.dlut.edu.cn/info/1019/4518.htm
Hotel: DUT International Conference Center (DUTICC) (neighbor to the South Gate of DUT), http://hotel.dlut.edu.cn/index_ch.asp
Conference Venue: Conference Room 2, DUT International Conference Center
Transportation: Taking a taxi is the easiest way from Dalian International Airport, or Dalian Train Station, or Dalian North Train Station to the hotel, and the taxi fare is about 30, 35, or 45 Chinese Yuan, respectively.
Sponsors: The workshop are supported in part by Dalian University of Technology, and grants (No.11329101 and No. 41171151) from NSFC.
Timetable
May 6, 2016; Venue: Conference Room 2, DUTICC
Speaker
Title
Chair
8:30-8:40
Opening Remarks
8:40-9:20
Yukio Matsumoto
Riemann surfaces and crystallographic groups
Andrei Yurievich Vesnin
9:20-10:00
Ki Hyoung Ko
Automorphism groups of a family of non-rigid Artin groups
10:00-10:20
Taking photo, Tea Time
10:20-11:00
ZHAO Xuezhi
On classification of cyclic orientation-reversing actions of big order on closed surfaces
11:00-11:40
Mikio Furuta
Seiberg-Witten theory, generalized (co)homology and TFT
11:50-13:30
Lunch Time
13:30-14:10
Andrey Yurievich Vesnin
On complexity and Turaev-Viro invariants of 3-manifolds
DUAN Haibao
14:10-14:50
Seiichi Kamada
Ribbon surface-links and clasp-ribbon surface-links
14:50-15:10
Tea Time
15:10-15:50
SONG Yongjin
Embedding problems of Artin groups of type E
HAN Youfa
15:50-16:00
16:00-16:20
JIN Xianan
A relation between the Tutte polynomial and the HOMFLY polynomial with applications in DNA polyhedra
GAO Hongzhu
16:20-16:40
Naoko Kamada
Converting virtual knot diagrams to normal diagrams
16:40-16:50
16:50-17:10
Jiming Ma
Hyperbolicity of a random link via bridge position
17:10-17:30
GUO xiao
Parabolic polynomials of 2-bridge knots
May 7, 2016; Venue: Conference Room 2, DUTICC
FANG Fuquan
Reflections in Riemannian manifolds
WU Jie
Kazuo Habiro
Category of handlebody embeddings
QIU Ruifeng
On distance of Heegaard splittings
Akio Kawauchi
Gyo Taek Jin
Examples and Counterexamples of the quadrisecant approximation conjecture
On a cross-section of an immersed sphere-link in 4-space
Velariy Bardakov
Some representations of virtual braid group by automorphisms
YANG Zhiqing
An infinite-variable knot invariant
YANG Wenyuan
Purely exponential growth of cusp-uniform actions
LIANG Liang
A sufficient condition for distance degenerating handle addtions to be bounded
ZOU Yanqing
The subset of $R^{3}$ realizing metrics on the curve complex
LU Zhi
LI Zhiguo
On the unknotting number of welded knots
Titles and Abstracts
Speaker: Velariy Bardakov (Novosibirsk State University, Russia)
Title: Some representations of virtual braid group by automorphisms
Abstract: Braid group B_n has a faithful representation in the automorphism group Aut(F_n) of free group F_n of rank n (Artin's representation). Using this representation, one cans define a group of link that is a strong invariant of a link. Virtual braid group VB_n is a generalization of braid group. This group is the foundation of the Virtual knot theory. We describe some known representations of VB_n into Aut(G_n) for some group G_n. After this we introduce a new representation which is generalized the previous representation. Using this representation we introduce the group of virtual link and prove that this group is an invariant of the link.
Speaker: FANG Fuquan(Capital Normal University, China)
Title: Reflections in Riemannian manifolds
Abstract:
Speaker: Mikio Furuta (University of Tokyo, Japan)
Title: Seiberg-Witten theory, generalized (co)homology and TFT
Abstract: Formulatons of Floer homotopy type for Seiberg-Witten theory are given by Manolescu, Manolescu-Kronheimer and Khandhawit-Lin-Sasahira. We will discuss two related topics.:(1) formulations of TFT for Seiberg-Witten theory using generalized (co)homology theories. (2) an approach to Seiberg-WItten FLoer homotopy type when an obstruction vanishes. (Joint works with Tian Jun Li (1), and Khandhawit and Sasahira (2)).
Speaker: Kazuo Habiro (Kyoto University, Japan)
Title: Category of handlebody embeddings
Abstract: I plan to talk about the category $H$ of handlebody embeddings. It has as objects nonnegative integers, and as morphisms from $m$ to $n$ embeddings of a handlebody of genus $m$ into a handlebody of genus $n$ modulo isotopy. Here embeddings and isotopies preserves "base discs" which are embedded disks in the boundaries of handlebodies. I will describe the braided monoidal category structure of $H$ and functors defined on $H$, which are regarded as invariants of handlebody embeddings.
Speaker: Gyo Taek Jin (KAIST, Korea)
Title: Examples and Counterexamples of the quadrisecant approximation conjecture
Abstract: We show smooth knots and polygonal knots, trivial and nontrivial, on which the quadrisecant approximation conjecture holds. We also show the counterexamples created by Bai-Wang-Wang, and discuss a possible modificaton of the conjecture.
Speaker: Seiichi Kamada (Osaka City University, Japan)
Title: Classification of 1-handles attaching to surface-links using quandles
Abstract: Classification of 1-handles attaching to surface-knots using groups was done by J. Boyle for oriented surface-knots, and by myself for non-orientable surface-knots. Here we discuss classification of 1-handles using quandles. We introduce the notion of the tensor product of quandles. Then 1-handles are naturally understood via the tensor product of the knot quandles, or the knot symmetric quandles.
Speaker: Akio Kawauchi (Osaka City University, Japan)
Title: On a cross-section of an immersed sphere-link in 4-space
Abstract: The torsion Alexander polynomial, the reduced torsion Alexander polynomial and the local signature invariant of a cross-section of an immersed sphere-link are investigated from the viewpoint of how to influence to the immersed sphere-link. It is shown that the torsion Alexander polynomial of a symmetric middle cross-section of a ribbon sphere-link is an invariant of the ribbon sphere-link. A generalization to a symmetric middle cross-section of an immersed ribbon sphere-link is given.
Speaker: Ki Hyoung Ko (KAIST, Korea)
Title: Automorphism groups of a family of non-rigid Artin groups
Abstract: An Artin group is rigid if its defining graph is unique. There have been extensive researches on automorphisms on rigid Artin groups such as Artin groups of finite types, free groups, and right-angled Artin groups. We will discuss automorphisms of a family of non-rigid Artin groups studied by John Crisp. In fact, we will completely determine the structures of automorphism groups of this family and this is one of the first results in this direction.
Speaker: Yukio Matsumoto (Gakushuin University, Japan)
Title: Riemann surfaces and crystallographic groups
Abstract: A crystallographic group is an isometry group acting on a Euclidean space $\mathbb{E}^n$ whose translation subgroup forms an $n$-dimensional lattice. For example, a so-called wall paper group is a two dimensional crystallographic group. This talk will report our recent discovery that certain crystallographic groups on $\mathbb{E}^{3g-3}$ naturally arize from Teichm\"uller space of Riemann surfaces of genus $g$.
Speaker: QIU Ruifeng (East China Normal University, China)
Title: On distance of Heegaard splitting
Abstract: In this talk, I will talk about some results on distance of Heegaard splitting, then try to explain why the definition "distance" led some important progresses on Heegaard splitting.
Speaker: SONG Yongjin (Inha University, Korea)
Title: Embedding problems of Artin groups of type E
Abstract: It was proved by Wajnryb that there is no geometric embedding of Artin groups of type E into mapping class group of surface. In this talk we will investigate the possibility of existence of nongeometric embedding of Artin groups of type E.
Speaker: Andrei Vesnin (Sobolev Institute of Mathematics, Novosibirsk, Russia)
Title: On complexity and Turaev-Viro invariants of 3-manifolds
Abstract: We will discuss new results on Matveev’s complexity of infinite families of orientable hyperbolic 3-manifolds. We will demonstrate how Turaev–Viro invariants of hyperbolic 3-manifolds with totally geodesic boundary can be used to find complexity of manifolds.
Speaker: YANG Zhiqing Dalian (University of Technology, China)
Title: An infinite-variable knot invariant
Abstract: This is a follow-up work of arXiv:1004.2085. The author modifed earlier work to get a stronger invariant. It uses a system of skein equations to define. It is a generalization of HOMFLY and Kauffman two variable polynomials. One simplified version of it is an infinite-variable HOMFLY polynomial.
Speaker: ZHAO Xuezhi (Capital Normal University, China)
Title: On classification of cyclic orientation-reversing actions of big order on closed surfaces
Abstract: At the end of 19 century, A. Wiman proved that the order of any orientation-preserving periodic self-homeomorphism of a closed orientable surface of genus $g >1$ does not exceed $4g+2$. Later in the 1960s, W. Harvey showed that this maximum possible order is attained for each $g$. In the middle of the 1980s, J. J. Etayo showed that any finite cyclic group $Z_N$ generated by an orienta\-tion-re\-ver\-sing periodic self-homeomorphisms of a closed orientable surface $S_g$ of genus $g>1$ has order bounded above by $4g+4$ and $4g-4$ for $g$ even and odd respectively, and these bounds are sharp for all $g$. Five years later, S. Wang proved these results more directly in a purely topological way. The question to which extent the constructions of Etayo and Wang are unique was the original motivation for the present paper. Here we classify up to topological conjugation orientation-reversing actions of a cyclic group $Z_N$ on $S_g$, in function of a possible type of the quotient orbifold $S_g/\Z_N$, provided that $N>2g-2$. In particular, we prove that Etayo-Wang extremal actions are unique up to topological conjugations.
Speaker: GUO Xiao (Harbin Institute of Technology, China)
Title: Parabolic polynomials of 2-bridge knots
Abstract: In the talk, I will introduce an algorithm for calculating the $p$-polynomials of $2$-bridge knots.
Speaker: JIN Xianan (Xiamen University, China)
Title: A relation between the Tutte polynomial and the HOMFLY polynomial with applications in DNA polyhedra
Abstract: Let $G$ be a plane graph. Let $D(G)$ be the oriented link obtained from $G$ by replacing each edge $e$ of $G$ by an alternatingly oriented 2-tangle $T_e$. We first establish a relation between the HOMFLY polynomial of $D(G)$ and the edge-weighted Tutte polynomial of $G$ by assigning suitable edge weights which depend on $T_e$'s or equivalently, the chain polynomial of $G$ with labels on edges of $G$. This relation extends works of F. Jaeger and L. Traldi. Then we apply the relation to DNA polyhedral links, the mathematical model for DNA polyhedra synthesized by chemists and biologists. To deal with complicated double crossover DNA 3-regular polyhedral links, another relation is further established for computing the chain polynomial of the truncated cubic graph with two different labels from the chain polynomial of the original labeled cubic graph by substitutions.
Speaker: Naoko Kamada (Nagoya City University, Japan)
Title: Converting virtual knot diagrams to normal diagrams
Abstract: A virtual knot diagram is said to be normal when the corresponding abstract knot diagram is checkerboard colorable. Not every virtual knot diagram is normal, while all classical knot diagrams are normal. In this talk we discuss a method of converting a virtual knot diagram to a normal virtual diagram. We discuss an invariant of a virtual knot that can be obtained from an invariant of the normal virtual diagram.
Speaker: LI Zhiguo(Dalian University of Technology, China)
Title: On the unknotting number of welded knots
Abstract: We discuss the unknotting number of welded knots, and give a upper-bound of the unknotting number of welded knots by using the warping degree method, and a lower bound of the unkotting number of welded knots by quandle colorings.
Speaker: LIANG Liang (Liaoning Normal University, China)
Title: A sufficient condition for distance degenerating handle addtions to be bounded
Abstract: Let $M = V\bigcup_{s} W$ be a Heegaard splitting of 3-manifold $M$ and $F$ a component of $\partial M$ lying in $\partial_{-}V$. A simple closed curve $J$ in $F$ is called to be distance degenerating if the distance of $M = V\bigcup_{s} W$ is less than the distance of $M_{J} = V_{J}\bigcup_{s} W$. In this report, I will introduce the handle additions and Heegaard splittings of 3-manifolds. At last, I
will give a result about distance degenerating handle additions. This is a joint work with Fengchun Lei and Fengling Li.
Speaker: MA Jiming (Fudan University, China)
Title: Hyperbolicity of a random link via bridge position
Abstract: We show that a random link via random bridge position is hyperbolic, this is a joint work with Kazuhiro Ichihara.
Speaker: YANG Wenyuan (Peking University, China)
Title: Purely exponential growth of cusp-uniform actions
Abstract: In this talk, I will discuss the purely exponential type of the orbit growth function with connections to the finiteness of Bowen-Margulis-Sullivan measures. Our setup is to consider a cusp-uniform action of a countable group on a $\delta$-hyperbolic space. The main result is characterizing the purely exponential growth type of growth by a condition introduced by Dal'bo-Otal-Peign\'e. This condition is equivalent to the finiteness of Bowen-Margulis-Sullivan measures on the unit tangent bundle of geometrically finite Cartan-Hadamard manifolds with pinched negative curvature. In this case, our result recovers a theorem of Roblin (in a coarse form).
Speaker: ZOU Yanqing (Dalian Nationalities University, China)
Title: The subset of $R^{3}$ realizing metrics on the curve complex
Abstract: It is known that the curve complex with the metric defined by Minsky and Masur is $\delta$-hyperbolic. Now we consider the possible metrics on the curve complex, which are built from a subset $V\subset R^{3}$, and discuss some properties of the curve complex under those new metrics. This is a joint work with Ruifeng Qiu and Faze Zhang.
School of Mathematical Sciences
Dalian University of Technology
Updated by April 25, 2016