You are here

Ring structures on singular instanton homology and link detection

Boyu Zhang (University of Maryland)
Wednesday, February 28, 2024 - 4:00pm to 5:00pm
PDL C-38

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 structures on singular instanton homology in C coefficients.  I will then present several applications of this computation in low-dimensional topology.  For example, using the properties of this ring structure on instanton homology, we can 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.

Event Type: