##### Department of Mathematics,

University of California San Diego

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### Math 292 - Topology Seminar

## Lisa Piccirillo

#### MIT

## Knot concordance and exotica

##### Abstract:

One well-known strategy for distinguishing smooth structures on closed 4-manifolds is to produce a knot $K$ in $S^3$ which is (smoothly) slice in one smooth filling $W$ of $S^3$ but not slice in some homeomorphic smooth filling $Wâ€™$. There are many techniques for distinguishing smooth structures on complicated closed 4-manifolds, but this strategy stands out for itâ€™s potential to work for 4-manifolds $W$ with very little algebraic topology. However, this strategy had never actually been used in practice, even for complicated $W$. Iâ€™ll discuss joint work with Manolescu and Marengon which gives the first application of this strategy. Iâ€™ll also discuss joint work with Manolescu which gives a systematic approach towards using this strategy to produce exotic definite closed 4-manifolds.

Host: Jianfeng Lin

### April 6, 2021

### 11:30 AM

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

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