Geometry and Topology Seminar

Symplectic Khovanov homology is an invariant of knots in S^3;
Heegaard Floer homology gives invariants of 3-manifolds and knots in
3-manifolds. Recently, Seidel-Smith gave spectral sequences relating
symplectic Khovanov homology and Heegaard Floer homology and relating the
symplectic Khovanov homology of a 2-periodic knot and its quotient.
Hendricks gave spectral sequences relating the Heegaard Floer homology of
a knot K in S^3 the preimage of K in the branched double cover, and
relating the Heegaard Floer homology of a 2-periodic knot and its
quotient.

In the first hour, we will review the construction of these invariants and
the associated spectral sequences, as well as a couple of new spectral
sequences obtained by similar constructions. The spectral sequences are
associated to equivariant Floer homology. In the second hour, we will give
another formulation of equivariant Floer homology and use the
reformulation to prove that the spectral sequences are invariants of the
corresponding topological data. The new content is joint with Hendricks
and Sarkar, and is inspired by work of Seidel-Smith and Seidel.