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K-State Today

November 13, 2014

Mathematics Colloquium lecture Nov. 13

By Reta McDermott

Kouichi Yasui, Hiroshima University and Michigan State University, will present "Corks and Exotic Smooth Structures on 4-Manifolds" as part of the Mathematics Department Colloquium lecture series at 2:30 p.m. Thursday, Nov. 13, in 122 Cardwell Hall.

The abstract for the lecture is: One of basic problems in 4-dimensional topology is to find exotic (i.e. homeomorphic but non-diffeomorphic) smooth structures on a given 4-manifold. It is known that every exotic smooth structure on any simply connected closed smooth 4-manifold is obtained by twisting a codimension zero contractible submanifold. Such contractible 4-manifolds are called corks, and they are useful object to study 4-manifolds. In this talk, I will explain various examples of cork structures on 4-manifolds and applications of corks to constructions of exotic 4-manifolds.

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