# The Second KAIST Geometric Topology Fair

### Hanhwa Resort Sorak, Sokcho, Kangwon, 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. Our main focus is knot theory and its relationship to manifold theory. We hope this workshop contributes to acceleration of research in the 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 Choi, Suhyoung KAIST Jeon, Choon Bae KAIST Jin, Gyo Taek KAIST Kim, Hun KAIST Kim, Jee Hyoun KAIST Kim, Jinhong KAIST Kim, Se-goo Kyonghee University

 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 Park, Hyo Won KAIST Song, Won Taek KIAS

## Programs

 February 17     February 18     February 19 Arrival and registration 6:30-8:00 --- Dinner --- 8:55-9:00 Announcements 9:00-9:40 Suhyoung Choi Real projective structures on 2- and 3-dimensional manifolds 9:50-10:30 Jae Choon Cha Algebraic closures with coefficients 10:40-11:20 Byoung Hee Ahn Representations of surface braid groups 11:30-12:10 Choon Bae Jeon Trisecants of spatial graph 12:10-1:30 --- Lunch --- 9:00-9:40 Se-Goo Kim On the 4-ball genus 9:50-10:30 Sang Jin Lee A new approach to the reducibility problem of braids 10:40-11:20 Won Taek Song Upper and lower bounds for the minimal positive entropy of pure braids 11:30-12:10 Sangyop Lee Exceptional Dehn fillings 12:10-1:30 --- Lunch ---

## Registration

Benefits for registeration include:
• Participation in the academic programs
• Rooms in the workshop venue (Hanwha Resort Sorak) for two nights, February 17 and 18
• Dinner on February 17 and lunches on February 18 and 19 (accompanying people are also welcome)
• ### Registration Fee

 Participants accompanied with family 130,000 Participants not accompanied with family 65,000 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 Sorak web page.

## Contact

Jae Choon Cha
Information and Communications University
103-6 Munji-dong Yuseong-gu
Daejeon 305-732, Korea
Phone: +82-42-866-6145
Email:

## Local information

In Hanwha Resort Sorak, there is a famous hot spring amusement park. More detailed information is available at Sorak Waterpia (in Korean).

## Abstracts

### Jae Choon Cha, Algebraic closures with coefficients

For any subring R of rationals, we construct R-coefficient algebraic closure of groups with respect to certain types of equations by generalizaing previous work of Jerome Levine. It turns out that this gives us a combinatorial description of the R-homology localization of groups. We discuss applications to link concordance, homology cobordism of compact manifolds, and derived filtrations of groups.

### Sang Jin Lee, A new approach to the reducibility problem of braids

Let $D_n$ be the $n$-punctured disc. We assume that it is a round disc and that the punctures lie on a line. An essential simple closed curve system in the punctured disc is \emph{standard} if each component is isotopic to a round circle. The $n$-braid group is a lattice under a subword-order and it acts on the set of essential curve systems in $D_n$. We show that given an essential curve system in $D_n$, the set of braids which make it standard is a sublattice. Using this, we make criterions for reducible braids so that each element in its ultra summit set has a standard reduction system.

### Sang Yop Lee, Exceptional Dehn fillings

We estimate the number of exceptional slopes for hyperbolic 3-manifolds with a torus boundary component and at least one other boundary component.

### Won Taek Song, Upper and lower bounds for the minimal positive entropy of pure braids

We show that the minimal positive entropy of pure braids is greater than $\log(2+\sqrt5)$, independently of the braid index. For pure 3-braids we show that the minimal entropy is equal to $\log(3+2\sqrt2)$.

HTML by Jae Choon Cha