低维拓扑学术报告
报告1
报 告 人：Professor Akio Kawauchi (Osaka City University, Japan)
报告题目：Characteristic Genera of Closed Orientable 3-Manifolds I
报告时间：2016年5月3日（星期二）下午3:30-4:30
报告地点：创新园大厦 A1101
报告2
报 告 人：Professor Akio Kawauchi (Osaka City University, Japan)
报告题目：Characteristic Genera of Closed Orientable 3-Manifolds II
报告时间：2016年5月5日（星期四）上午9:30-10:00
报告地点：创新园大厦 A1101
报告摘要：A complete invariant defined for (closed connected orientable) 3-manifolds is an invariant defined for the 3-manifolds such that any two 3-manifolds with the same invariant are homeomorphic. Further, if the 3-manifold itself can be reconstructed from the data of the complete invariant, then it is called a characteristic invariant defined for the 3-manifolds. In a previous work, a characteristic lattice point invariant defined for the 3-manifolds was constructed by using an embedding of the prime links into the set of lattice points. In this paper, a characteristic rational invariant defined for the 3-manifolds called the characteristic genus defined for the 3-manifolds is constructed by using an embedding of a set of lattice points called the PDelta set into the set of rational numbers. The characteristic genus defined for the 3-manifolds is also compared with the Heegaard genus, the bridge genus and the braid genus defined for the 3-manifolds. By using this characteristic rational invariant defined for the 3-manifolds, a smooth real function with the definition interval (-1,1) called the characteristic genus function is constructed as a characteristic invariant defined for the 3-manifolds.
报告人简介：Professor Akio Kawauchi (Specially Appointed Professor; Honorary Professor of Osaka City University & Honorary Director of Osaka City University Advanced Mathematical Institute) is a specialist of knot theory, writing more than 100 papers, and well-known as the author of the book "A Survey of Knot Theory" (Birkh\"auser,1996). In his earlier work, the determination of non-invertibility of the knot 8_17 (which has been standing as an unsolved problem for 50 years) is noted. In recent works, the affirmative solution of smooth unknotting conjecture of a ribbon 2-knot (which has been standing as an unsolved problem for 45 years) and the result that all the closed orientable 3-manifolds are classified by a one-variable real analytic function (which will be explained in the lectures) are noted.
报告3
报 告 人：Professor Seiichi Kamada (Osaka City University, Japan)
报告题目：Ribbon surface-links and clasp-ribbon surface-links
报告时间：2016年5月5日（星期四）上午10:20-11:20
报告地点：创新园大厦A1101
报告摘要：Ribbon surface-links are a special family of surface-links. They bound handlebodies in 4-space with ribbon singularities. We generalize them to clasp-ribbon surface-links, that bound handlebodies in 4-space with clasp or ribbon singularities. We discuss normal forms of these surface-links. This is a joint work with Kengo Kawamura.
报告人简介：Seiichi Kamada is a professor of Department of Mathematics, Osaka City University and the vice-director of the Osaka City University Advanced Mathematical Institute.He has been working on low dimensional topology, including the follows: knot theory, two-dimensional knots, surface-links in 4-space, braids, 2-dimensional braids, surface braids, virtual knot theory, quandle homology theory, quandle cocycle invariants, Lefschetz fiberations of 4-manifolds, braid monodromies and their Hurwitz equivalences. He is one of the managing editors of the Journal of Knot Theory and Its Ramifications, and a member of the program committee of the sereies of annual international conferences “East Asian School of Knots and Related Topics”
报告4
报 告 人：Professor Andrei Vesnin (Sobolev Institute of Mathematics, Novosibirsk, Russia)
报告题目：Tetrahedral hyperbolic 3-manifolds: census and properties
报告时间：2016年5月9日（星期一）下午2:30-3:30
报告地点：创新园大厦A1101
报告摘要：A cusped hyperbolic 3-manifold is called tetrahedral if it can be decomposed in a finite number of ideal regular hyperbolic tetrahedral. Among examples of tetrahedral manifolds are the figure-eight knot complement and the Gieseking manifold. We will discuss some interesting properties of tetrahedral manifolds and present a census of orientable and non-orientable tetrahedral manifolds.
报告人简介: Prof. Andrei Vesnin is head of the Laboratory of Applied Analysis, Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences and a professor of Geometry and Topology, Novosibirsk State University. He received a Candidate of Sciences in physics and mathematics is 1991 from Sobolev Institute of Mathematics for the thesis ”Discrete groups of reflections and three-dimensional manifolds”, and a Doctor of Sciences in physics in mathematics in 2005 for the thesis ”Volumes and isometries of three-dimensional hyperbolic manifolds and orbifolds”. He was a visiting professor in Seoul National University in 2002 – 2004.
Prof. Vesnin's reseach interests include low-dimensional topology, knot theory, hyperbolic geometry, combinatorial group theory, graph theory and applications.
In 2008 Prof. Vesnin was elected to corresponding member of the Russian Academy of Sciences.
Prof. Vesnin is the editor-in-chief of Siberian Electronic Mathematics Reports and a member of editorial boards of Siberian Mathematical Journal and Scientiae Mathematicae Japonicae.
报告5
报 告 人：Professor Velariy Bardakov (Novosibirsk State University, Russia)
报告题目：Some quotients of Virtual knot theory and classifications of fused links I
报告时间：2016年5月9日（星期一）下午3:40-4:40
报告地点：创新园大厦A1101
报告6
报 告 人：Professor Velariy Bardakov (Novosibirsk State University, Russia)
报告题目：Some quotients of Virtual knot theory and classifications of fused links I
报告时间：2016年5月16日（星期一）下午3:40-4:40
报告地点：创新园大厦A1101
报告摘要：There are some quotients of Virtual knot theory: Welded knot theory, Fused knot theory and so on. Welded knot theory is the quotient of Virtual knot theory by the first forbidden move. The group of welded braids WB_n is a quotient of virtual braid group VB_n and is isomorphic to subgroup
the automorphism group Aut(F_n) of free group F_n of rank n. We discuss some properties of this group. Fused knot theory is the quotient of Virtual knot theory by the both forbidden moves. Well known that any fused knot is trivial, but it is not true for links. The problem of classification of fused links is arrived. There are some approaches to solution of this problem. We will give this classification using group of fused link.
报告人简介：Prof. Professor Velariy Bardakov is a Professor of Sobolev Institute of Mathematics and Novosibirsk State University. His reearch interests include Algebra, Group Theory, Low Dimension Topology, Knot Theory.
报告校内联系人：雷逢春 联系电话：84706472
大连理工大学数学科学学院
2016年3月30日
