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.

Choe, Jaigyoung (KIAS)

Hwang, Jun-Muk (KIAS)

Keum, JongHae (KIAS)

Park, Jongil (Seoul National Univ.)

09:50-10:00 | Opening address | |

10:00-10:50 | JongHae Keum |
Quotients of fake projective planes |

10:50-11:10 | -- Coffee Break -- | |

11:10-12:00 | Jun-Muk Hwang |
Deformation of holomorphic maps onto Kaehler manifolds |

12:00-02:00 | -- Lunch -- | |

02:00-02:50 | Jaigyoung Choe |
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 |

04:20-05:10 | Jongil Park |
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

Phone: 02-450-3407

Email: sangjin@konkuk.ac.kr

Webpage: http://home.konkuk.ac.kr/~sangjin