Gauge Theory and Topology: Skein exact triangles in equivariant singular instanton theory

Gauge Theory and Topology Seminar, SEMINARS

Speaker:

Christopher Scaduto - University of Miami

Given a knot or link in the 3-sphere, its Murasugi signature is an integer-valued invariant which can easily be computed from a diagram. Work of Herald and Lin gives an alternative description of knot signatures, as signed counts of SU(2)-representations of the knot group which are traceless around meridians. There is a version of singular instanton homology for links which categorifies the Murasugi signature. We construct unoriented skein exact triangles for these Floer groups, categorifying the behavior of the Murasugi signature under unoriented skein relations. More generally, we construct skein exact triangles in the setting of equivariant singular instanton theory. This is joint work with Ali Daemi.