Joint Topology Seminar

Abstract. The fixed-point Floer homology of a symplectomorphism gives a lower bound for the number of fixed points of non-degenerate representatives of its Hamiltonian isotopy class. It's usually hard to compute. Seidel (2001) conjectured a description of the Floer homology of a composite of Dehn twists along Lagrangian spheres. I'll give a concrete formulation of the conjecture,and a status-report on my efforts to prove it. This formulation involves a "hypercube" chain complex, similar (and perhaps in some cases isomorphic) to structures appearing in Heegaard Floer homology and in Khovanov homology.