Deformed Hamiltonian Floer theory, capacity estimates and Calabi quasimorphisms

作者：Usher Michael^*

来源：Geometry and Topology, 2011, 15(3): 1313-1417.

DOI：10.2140/gt.2011.15.1313

We develop a family of deformations of the differential and of the pair-of-pants product on the Hamiltonian Floer complex of a symplectic manifold (M, omega) which upon passing to homology yields ring isomorphisms with the big quantum homology of M. By studying the properties of the resulting deformed version of the Oh-Schwarz spectral invariants, we obtain a Floer-theoretic interpretation of a result of Lu which bounds the Hofer-Zehnder capacity of M when M has a nonzero Gromov-Witten invariant with two point constraints, and we produce a new algebraic criterion for (M, omega) to admit a Calabi quasimorphism and a symplectic quasistate. This latter criterion is found to hold whenever M has generically semisimple quantum homology in the sense considered by Dubrovin and Manin (this includes all compact toric M), and also whenever M is a point blowup of an arbitrary closed symplectic manifold.

• 出版日期2011