Abstract
Two commuting symplectomorphisms of a symplectic manifold give rise to actions on Floer cohomologies of each other. We prove the elliptic relation saying that the supertraces of these two actions are equal. In the case when a symplectomorphism $f$ commutes with a symplectic involution, the elliptic relation provides a lower bound on the dimension of $HF^*(f)$ in terms of the Lefschetz number of $f$ restricted to the fixed locus of the involution. We apply this bound to prove that Dehn twists around vanishing Lagrangian spheres inside most hypersurfaces in Grassmannians have infinite order in the symplectic mapping class group.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have