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 |
| 9:00-9:40 | Gyo Taek Jin | Quadrisecant approximation of knots | |
| 9:50-10:30 | Jae Choon Cha | Abelian invariants of periodic knots from quotient links | |
| 10:40-11:20 | Sangyop Lee | Toroidal Dehn surgeries on knots in S^1xS^2 | |
| 11:30-12:10 | Won Taek Song | On the conjugacy problem of pseudo-Anosov surface homeomorphisms | |
| 12:10-1:30 | | Lunch | |
| 1:30-2:10 | Sang Jin Lee | Roots and powers of elements in Garside groups | |
| 2:20-3:00 | Youngsik Huh | Finite planar graphs and trivializability | |
| 3:10-3:50 | Se-goo Kim | Alexander polynomials and orders of homology groups | |
| 3:50-4:30 | | Break | |
| 4:30-4:50 | Jang Won Lee | TBA | |
| 4:50-5:10 | Byoung Hee An | TBA | |
| 5:10-5:30 | Jung Hun Lee | TBA | |
|
| 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.