제 2회 Topology Workshop
8월 17일(월)-19일(수)
장소: #1501, E6-1, KAIST
Invited Speaker
김태희(건국대) 서동엽(KAIST)
송용진(인하대) 이종범(서강대)
정규락(KIAS) 조윤희(서울시립대)
조장현(경상대) 조진석(서울대) 함지영(서울대)
주관: 송용진(인하대학교), 서동엽(KAIST)
* 17일 점심이 예약되어 있으니 일찍 도착하시는 분들께서는
자연과학동 E6-1 #1410 에 11시 50분까지 오셔서 식권을 받아 이용하시기 바랍니다.
문의:
송용진 : yjsong@inha.ac.kr, HP : 011-477-9294
김윤옥 : yokim@kaist.ac.kr, Tel : 042-350-8111
**PROGRAM** The second TOPOLOGY WORKSHOP
August 17 -19, 2009, KAIST
8월 17일 (월)
1:00 – 1:15 등록 및 개회식
**Bott towers and cohomological rigidity I**
A Bott tower is a sequence of CP1-bundles Bi over Bi-1. Each Bi is a called the i-th stage Bott manifold. One
can extend this definition to define a generalized Bott tower and manifold to be a sequence of complex space
bundles. One of the interesting question in toric topology asks whether two (generalized) Bott manifolds Bn
and Bn' are homeomorphic (or diffeomorphic) provided their cohomologies are isomorphic as graded rings.
This is called the cohomological rigidity question} for (generalized) Bott manifolds. In this talk we discuss
some related back ground material from toric theory and some positive results on the question.
**Averaging formula for Nielsen numbers I**
We show that the averaging formula for Nielsen numbers holds for continuous maps on infranilmanifolds, and
infra-solvmanifolds of type (R). We illustrate by examples how practical the formula is.
**Derived (or Homotopy) categories and derived functors I**
Mathematical invariants may be represented as fuctors from categories to categories but many invariants are
homotopy invariants. So we consider their derived categories and their derived functors instead. I will explain
this process and give some examples.
**Finitely dominated spaces and projective modules I**
In this talk, I will survey various results in the topic indicated by the title and introduce its related several
algebraic or topological conjectures. I will also present various topics such as finiteness conditions of groups,
L2-invariants, and etc.
**Finitely dominated spaces and projective modules II**
In this talk, I will survey various results in the topic indicated by the title and introduce its related several
algebraic or topological conjectures. I will also present various topics such as finiteness conditions of
groups, L2-invariants, and etc. 6:30 회식 (Dinner)
8월 18일 (화)
**Bott towers and cohomological rigidity II**
A Bott tower is a sequence of CP1-bundles Bi over Bi-1. Each Bi is a called the i-th stage Bott manifold. One
can extend this definition to define a generalized Bott tower and manifold to be a sequence of complex space
bundles. One of the interesting question in toric topology asks whether two (generalized) Bott manifolds Bn
and Bn' are homeomorphic (or diffeomorphic) provided their cohomologies are isomorphic as graded rings.
This is called the cohomological rigidity question} for (generalized) Bott manifolds. In this talk we discuss
some related back ground material from toric theory and some positive results on the question.
**Averaging formula for Nielsen numbers II**
We show that the averaging formula for Nielsen numbers holds for continuous maps on infranilmanifolds,
and infra-solvmanifolds of type (R). We illustrate by exampleshow practical the formula is.
**Derived (or Homotopy) categories and derived factors II**
Mathematical invariants may be represented as fuctors from categories to categories but many invariants are
homotopy invariants. So we consider their derived categories and their derived functors instead. I will explain
this process and give some examples.
12:00-1:00 점심
1:00~ 단체 관광 (Excursion) 장소: 부여
8월 19일 (수)
**Kashaev invariant**
We will briefly overview some basic theory of knots and quantum invariants. As an example of quantum
invariants, we will define the Kashaev invariant of a knot.
**Kashaev's volume conjecture** Kashaev conjectured that the limit of the Kashaev invariant of a knot gives
the hyperbolic volume of the knot complement. We will overview some geometric meanings of the Kashaev
invariant following Yokota theory. Some recent improvements in the volume conjecture will be briefly
discussed.
**Problems in extended hyperbolic space I**
We define and study an extended hyperbolic space which contains the hyperbolic space and de Sitter
space as subspaces and which is obtained as an analytic continuation of the hyperbolic space. We discuss
extended Kleinian model and extended Poincare model. And we discuss the advantages of this new
geometric model as well as some of its applications and problems.
12:15-1:45 Lunch
**Reidemeister torsion and homology cylinders I**
In these two lectures, we will discuss Reidemeister torsion and its application to homology cylinders over a
surface. In the first lecture, an algebraic definition of Reidemeister torsion will be given, and we will study its
basic properties. Using these, in the second lecture we will show that the homology cobordism group of
homology cylinders over a surface has nontrivial abelian quotients, which is joint work with Jae Choon Cha
and Stefan Friedl.
**Reidemeister torsion and homology cylinders II**
In these two lectures, we will discuss Reidemeister torsion and its application to homology cylinders over
a surface. In the first lecture, an algebraic definition of Reidemeister torsion will be given, and we will study
its basic properties. Using these, in the second lecture we will show that the homology cobordism group of
homology cylinders over a surface has nontrivial abelian quotients, which is joint work with Jae Choon Cha
and Stefan Friedl.
Volumes of hyperbolic cone-manifolds of knot 6_1 |