Symplectic Khovanov homology of periodic links

Sriram Raghunath (Rutgers)

Abstract: When a knot diagram is symmetric, it induces an action on the Khovanov chain complex of the knot. We can analyze the equivariant cohomology of the chain complex with respect to this action to understand relationships between the Khovanov homology of the original knot and the Khovanov homology of the quotient knot. Stoffregen and Zhang have studied the extension of this action to the Khovanov homotopy type and applied Smith theory to prove results about periodic knots, while Lipshitz and Sarkar have used the same techniques to understand the Khovanov homology of strongly invertible knots. Seidel and Smith have defined a symplectic reformulation of combinatorial Khovanov homology, and they have used localization techniques in Floer theory to study the symplectic Khovanov homology of 2-periodic knots. In our work, we define an annular version of symplectic Khovanov homology and apply this theory to investigate the symplectic Khovanov homology of 2-periodic and strongly invertible knots. This talk is based on joint work with Kristen Hendricks and Cheuk Yu Mak.