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

Classification of n-component links with Khovanov homology of rank 2^n - Boyu Zhang

Boyu Zhang
February 24, 2020

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.