Skein Exact Triangles in Equivariant Singular Instanton Theory

Explore a 59-minute lecture on Skein Exact Triangles in Equivariant Singular Instanton Theory presented by Christopher Scaduto from the University of Miami. Delve into the alternative description of knot signatures as signed counts of SU(2)-representations of the knot group, which are traceless around meridians. Discover how singular instanton homology for links categorifies the Murasugi signature. Learn about the construction of unoriented skein exact triangles for these Floer groups and their generalization in equivariant singular instanton theory. Follow the lecture's progression through topics such as reducibles, quasi-orientations, preferred and distinguished meridians, holonomy fixing, and the equivariant approach. Examine the chain complex, differential, irreducible homology, and conjectural homology. Conclude with an exploration of exact triangles, suspension, and the main theorem of this joint work with Ali Daemi.