Abstract:
In this talk, I will present an excision formula for singular instanton Floer homology where the excision surfaces intersect the singular locus. This formula allows us to define an instanton Floer homology theory for sutured manifolds with tangles. Similar to the non-singular case, the instant Floer homology for tangles is non-vanishing on taut manifolds with tangles and detects trivial products. As applications, we prove several detection results for Khovanov homology. This is joint work with Yi Xie.