The First KAIST Geometric Topology Fair

A workshop on geometric topology
including knot theory, manifold theory, and related topics

August 24-26, 2004

Hanhwa Resort Suanbo, Chungju, Chungbuk, Korea

The aim of this workshop is to encourage academic activities in the area of geometric topology in Korea and promote friendly relations between researchers in this area. This year we focus on knot theory and low-dimensional manifolds. We hope this workshop contributes to acceleration of research in this field.

Organizers

Ki Hyoung Ko (KAIST), Gyo Taek Jin (KAIST), and Jae Choon Cha (ICU)

Confirmed Participants

An, Byung Hee KAIST
Cha, Jae Choon ICU
Cho, Mi Sung KAIST
Huh, Young Sik Hanyang University
Jin, Gyo Taek KAIST
Kim, Hun KAIST
Kim, Jee Hyoun KAIST
Kim, Se-goo University of California, Santa Babara
Ko, Ki Hyoung KAIST
Lee, Gye Seon KAIST
Lee, Hwa Jeong KAIST
Lee, Jang Won KAIST
Lee, Jung Hun KAIST
Lee, Sang Jin Konkuk University
Lee, Sangyop KIAS
Oh, Seungsang Korea University
Park, Hyo Won KAIST
Song, Won Taek KIAS

Programs

August 24     Arrival and registration
August 25
9:00-9:40Gyo Taek JinQuadrisecant approximation of knots
9:50-10:30Jae Choon ChaAbelian invariants of periodic knots from quotient links
10:40-11:20 Sangyop LeeToroidal Dehn surgeries on knots in S^1xS^2
11:30-12:10    Won Taek Song    On the conjugacy problem of pseudo-Anosov surface homeomorphisms
12:10-1:30Lunch
1:30-2:10Sang Jin LeeRoots and powers of elements in Garside groups
2:20-3:00Youngsik HuhFinite planar graphs and trivializability
3:10-3:50Se-goo KimAlexander polynomials and orders of homology groups
3:50-4:30Break
4:30-4:50Jang Won LeeTBA
4:50-5:10Byoung Hee AnTBA
5:10-5:30Jung Hun LeeTBA
August 26 Departure

Registration

Benefits for registeration include:
  • Rooms in the workshop venue (Hanwha Resort Suanbo) for two nights, August 24 and 25
  • Dinner on August 24, Lunch and Dinner on August 25
  • Registration Fee

    Participants accompanied with family 120,000
    Participants not accompanied with family 60,000
    Students and unemployed 30,000
    (Korean Won)

    Very limited funding may be available to those not supported by other grants. Please contact the organizers (see the contact information below).

    Accomodations

    We have reserved a block of rooms for participants. We welcome your family; for more comfortable stay, we will assign to each family a guest house with a bedroom, living room, kitchen, and bathroom. Participants not accompanied with family, students, and unemployed participants will share rooms of the same type. For more information on rooms please see Hanwha Resort Suanbo web page.

    Contact

    For any inquiries on the workshop, please contact:

    Jae Choon Cha
    Information and Communications University
    119 Munjiro Yuseong-gu, Daejeon 305-714, Korea
    Phone: +82-42-866-6145
    Email:

    Local information

    Suanbo Hot Spring (Korean)

    Abstracts

    Jae Choon Cha, Abelian invariants of periodic knots from quotient links

    We study of abelian invariants of quotient links of periodic knots. We extract equivariant concordance invariants from unlocalized Blanchfield forms and Alexander polynomials. As a consequence we prove the Davis-Naik conjecture on the Murasugi polynomial of equivariant slice knots. We also show that our invariants are stronger than previously known abelian invariants of periodic knots. Finally we define a signature invariant of periodic knots via a homomorphism of a certain relative L-group.

    Gyo Taek Jin, Quadrisecant approximation of knots

    If a knot K has n quadrisecants, they cut K into at most 4n arcs. Straightening each of the arcs with end points fixed, we obtain a possibly singular polygonal knot \widehat K which we will call the quadrisecant approximation of K. Experiments show that quadrisecant approximations are genuine knots of the same knot types.

    Sang Jin Lee, Roots and powers of elements in Garside groups

    The Garside group, introduced by Dehornoy and Paris, is a generalization of the Artin groups of finite type. We show that the semidirect products of Garside monoids are Garside monoids. Then we present two results. First, the problem of finding roots of elements in a Garside group can be reduced to the conjugacy problem in a wreath product of the group, which improves the previous results of Styshnev and Sibert. Second, the set of translation numbers of elements in a Garside group is a discrete set, which gives an affirmative answer to the question of Gersten and Short at least for the Garside groups.

    Sangyop Lee, Toroidal Dehn Surgeries on Knots in S^1 x S^2

    Given a simple manifold, we investigate two Dehn fillings one of which contains a non-separating sphere and the other contains an essential torus.

    Won Taek Song, On the conjugacy problem of pseudo-Anosov surface homeomorphisms

    We present an algorithmic solution to the conjugacy problem in the mapping class group for pseudo-Anosov homeomorphisms. We use the set of train track representatives each of which admits only one folding operation. We call them ufers (unique folding efficient representatives). We define a cycling operation which produces another ufer from a ufer. The set of ufers mod surface homeomorphisms (which is a complete conjugacy invariant) is a union of cycles, which are connected to each other by sequences of folding operations and their inverses.