##### Department of Mathematics,

University of California San Diego

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### Math 292 - Topology Seminar

## Kyle Hayden

#### Columbia University

## Surfaces in 4-manifolds behaving badly

##### Abstract:

Corks are special contractible 4-manifolds that play a key role in the study of exotic smooth 4-manifolds. In this talk, I will describe applications of corks to the study of surfaces in 4-manifolds. I'll begin with some badly behaved 2-spheres in 4-space, based on joint work with Piccirillo. Then I'll use a twist on these ideas to construct smoothly (indeed, holomorphically) embedded disks in the 4-ball that are isotopic through ambient homeomorphisms but not through diffeomorphisms. There will be lots of cartoons.

Host: Jianfeng Lin

### November 24, 2020

### 10:30 AM

### Zoom information: Meeting ID: 933 6734 4286 Password: topology

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