Gauge Theory and Topology: Arnold conjecture and refinements of Floer homology

Gauge Theory and Topology Seminar, SEMINARS

Speaker:

Shaoyun Bai - Simons Center

We show that for any closed symplectic manifold, the number of 1-periodic orbits of any non-degenerate Hamiltonian is bounded from below by an integral version of total Betti number which takes account of torsions of all characteristics. The proof is based on a perturbation scheme (FOP perturbations) which produces pseudo-cycles from normally complex derived orbifolds, and a regularization procedure of moduli spaces of J-holomorphic curves (extending recent work of Abouzaid-McLean-Smith) which produces coherent smooth structures on the moduli spaces of Floer trajectories. I will outline the proof and indicate how these results may fit into other topics including Floer homotopy theory. This is based on joint work with Guangbo Xu.