Last updated on October 17th, 2006.
2006 Geometry & Topology Day at Konkuk University
November 18, 2006
Konkuk University, Seoul, Korea
The aim of this workshop is to encourage academic activities in the area of
geometry and topology in Korea and promote friendly relations between researchers
in this area.
OrganizersSung-Eun Koh, Dosang Joe and Sang Jin Lee
Cha, Jae Choon (ICU)
Choe, Jaigyoung (KIAS)
Hwang, Jun-Muk (KIAS)
Keum, JongHae (KIAS)
Park, Jongil (Seoul National Univ.)
All lectures will be in Room 201 of the College of Science at Konkuk University.
||Quotients of fake projective planes|
|10:50-11:10||-- Coffee Break -- |
||Deformation of holomorphic maps onto Kaehler manifolds|
|12:00-02:00||-- Lunch -- |
||Total curvatures in differential geometry|
|02:50-03:20||-- Coffee Break -- |
|03:20-04:10||Jae Choon Cha
|| Invariants from Atiyah type theorems and applications to links|
||A note on simply connected 4-manifolds with b_2^+=1|
- JongHae Keum: Quotients of fake projective planes
A fake projective plane is a compact complex surface with the same Betti numbers as the complex projective plane,
but not isomorphic to it. By a result of Yau, such a surface must have the 2-dimensional complex ball as its universal cover,
hence its fundamental group must be an infinite group.
Some fake projective planes may have a nontrivial automorphism of finite order, and its quotient seems to give a very interesting algebraic surface.
For example, if the order of the automorphism is 3, then the minimal resolution of the quotient is a minimal surface of general type
with K^2=3 and with no global holomorphic differential 1- or 2-forms.
We will discuss geometric properties of all possible quotients of fake projective planes.
- Jun-Muk Hwang: Deformation of holomorphic maps onto Kaehler maifolds
In a collaboration with S. Kebekus and T. Peternell, we had shown
that essentially all deformations of holomorphic maps onto a projective algebraic manifold
of non-negative Kodaira dimension come from automorphisms of the target.
In a recent joint work with T. Peternell, we extended the result to Kaehler manifolds.
Since the proof of the algebraic case used Miyaoka's result proved by characeristic p method,
the Kaehler case requires a new idea. This is provided by the study of torus actions.
- Jaigyoung Choe: Total curvatures in differential geometry
Three types of total curvatures will be reviewed: Gauss-Kronecker, Chern-Lashof,
and Chern-Gauss-Bonnet. We prove a relationship between Gauss-Kronecker and Chern-Lashof, and propose a possible application to minimal submanifolds.
- Jae Choon Cha: Invariants from Atiyah type theorems and applications to links
It is known that a signature defect invariant of 3-manifolds
is obtained from the index theory due to Atiyah and Singer. We
generalizes it to an L-theory invariant of 3-manifolds by proving a
Atiyah-type theorem for Witt classes of certain intersection forms of
4-manifolds. Considering the case of homology localization
coefficients, we give some applications to slicing links.
- Jongil Park: A note on simply connected 4-manifolds with b_2^+=1
In this talk we review the geography
- the existence and the uniqueness - problems of simply connected 4-manifolds
with b_2^+=1 in three levels; smooth category, symplectic category and complex category.
For any inquiries on the workshop, please contact
Prof. Sang Jin Lee
Dept. Math., Konkuk University
1 Hwayang-dong, Gwangjin-Gu, Seoul Korea