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Geometry and Topology Seminar

Friday, October 23, 2020
3:00pm to 4:00pm
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Several detection results of Khovanov homology on links
Boyu Zhang, Department of Mathematics, Princeton University,

The Khovanov homology is a combinatorially defined invariant for knots and links. I will present several new detection results of Khovanov homology on links. In particular, we show that if L is an n-component link with Khovanov homology of rank 2^n, then it is given by the connected sums and disjoint unions of unknots and Hopf links. This result gives a positive answer to a question asked by Batson-Seed, and it generalizes the unlink detection theorem by Hedden-Ni and Batson-Seed. The proof relies on a new excision formula for the singular instanton Floer homology. This is joint work with Yi Xie.

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