Monday

The singular instanton Floer homology of S^1 times a surface has a natural ring structure given by the pair-of-pants cobordisms. The study of this ring structure and related questions has a long history that can be dated back to the work of Atiyah and Bott. In this talk, I will present a complete characterization of the ring structure on singular instanton homology in C coefficients. I will then present several applications of this computation in the study of knots and links. For example, we show that if L is a link in S^3 that is not the unknot or the Hopf link, then the fundamental group of the complement of L has an irreducible SU(2) representation; we also give a complete classification for links whose Khovanov homology have the minimal possible rank.