##### Department of Mathematics,

University of California San Diego

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### Math 292 - Topology

## Boyu Zhang

#### Princeton University

## Classification of n-component links with Khovanov homology of rank $2^n$

##### Abstract:

Suppose $L$ is a link with n components and the rank of $Kh(L;Z/2)$ is $2^n$, we show that $L$ can be obtained by disjoint unions and connected sums of Hopf links and unknots. This result gives a positive answer to a question asked by Batson-Seed, and generalizes the unlink detection theorem of Khovanov homology by Hedden-Ni and Batson-Seed. The proof relies on a new excision formula for the singular instanton Floer homology introduced by Kronheimer and Mrowka. This is joint work with Yi Xie.

Host: Jianfeng Lin

### January 21, 2020

### 9:30 AM

### AP&M 7218

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