2010/06/30 by Michael Usher · 1 citation
Mathematics · #math.SG #msc:53D40 #msc:53D45
paper · pdf · doi:10.2140/gt.2011.15.1313
published as Geom. Topol. 15 (2011) 1313-1417 · 73 pages, 1 color figure. Added new material explaining how to make some of the constructions on semipositive manifolds without using Kuranishi structures
arxiv created 2011/08/05 · arxiv updated 2014/11/11
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,ω) 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,ω) to admit a Calabi quasimorphism and a symplectic quasi-state. 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.