The Second KAIST Geometric Topology Fair

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

February 17-19, 2005

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.


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


February 17     Arrival and registration
6:30-8:00--- Dinner ---
February 18     8:55-9:00Announcements
9:00-9:40Suhyoung ChoiReal projective structures on 2- and 3-dimensional manifolds
9:50-10:30Jae Choon ChaAlgebraic 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 ---
February 19     9:00-9:40Se-Goo KimOn the 4-ball genus
9:50-10:30Sang Jin LeeA new approach to the reducibility problem of braids
10:40-11:20 Won Taek SongUpper and lower bounds for the minimal positive entropy of pure braids
11:30-12:10    Sangyop LeeExceptional Dehn fillings
12:10-1:30 --- Lunch ---


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).


    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.


    For any inquiries on the workshop, please contact:

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

    Local information

    For more information on the hotel, please see Hanwha Resort Sorak (in Korean).

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


    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