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 Kronheimer and Mrowka's singular instanton Floer homology.

This is joint work with Yi Xie.