Boyu Zhang (Princeton)

Title: Excision for singular instanton Floer homology and applications

Abstract: In this talk, we will introduce an excision theorem for the instanton Floer homology that allows the excision surface to intersect the singularity. We will use it to construct an instanton Floer homology for tangles on sutured manifolds. As applications, we will answer a question asked by Batson and Seed about the classification of links whose Khovanov homology have minimal rank; we will also show that the annular Khovanov homology (1) detects the unlink, (2) detects the closure of the trivial braid, and (3) distinguishes braid closures from other links. This is joint work with Yi Xie.