Functors and Computations in Floer homology with Applications Part II

Abstract

The results in this paper concern computations of Floer cohomology using generating functions. The first part proves the isomorphism between Floer cohomology and Generating function cohomology introduced by Lisa Traynor. The second part proves that the Floer cohomology of the cotangent bundle (in the sense of Part I), is isomorphic to the cohomology of the loop space of the base. This has many consequences, some of which were given in Part I (GAFA, Geom. funct. anal. Vol. 9 (1999) 985-1033), others will be given in forthcoming papers. The results in this paper had been announced (with indications of proof) in a talk at the ICM 94 in Z{ü}rich. Up to typos, this is the revised version from 2003.

Version revised in 2003

Cited by in corpus (28)

• Fukaya categories and deformations
• Maximal contact and symplectic structures
• Cyclic homology, $S^1$-equivariant Floer cohomology, and Calabi-Yau structures
• Orlov and Viterbo functors in partially wrapped Fukaya categories
• Symplectic Banach-Mazur distances between subsets of C^n
• Homological mirror symmetry for Milnor fibers of simple singularities
• Floer theory of disjointly supported Hamiltonians on symplectically aspherical manifolds
• Homotopy type of the unitary group of the uniform Roe algebra on ${\mathbb{Z}}^n$
• Symplectic homology of convex domains and Clarke's duality
• Contact orderability up to conjugation
• On periodic points of Hamiltonian diffeomorphisms of $\mathbb{C}{\text{P}}^d$ via generating functions
• Remarks on symplectic capacities of $p$-products
• Loop coproduct in Morse and Floer homology
• Poincaré duality for loop spaces
• Monodromy of monomially admissible Fukaya-Seidel categories mirror to toric varieties
• Versality in mirror symmetry
• Time-periodic solutions of Hamiltonian PDEs using pseudoholomorphic curves
• Exact Calabi-Yau categories and odd-dimensional Lagrangian spheres
• The sharp energy-capacity inequality on convex symplectic manifolds
• Persistence modules, symplectic Banach-Mazur distance and Riemannian metrics
• Spectral spread and non-autonomous Hamiltonian diffeomorphisms
• The equivariant pair-of-pants product in fixed point Floer cohomology
• On the minimal symplectic area of Lagrangians
• An intertwining relation for equivariant Seidel maps
• Legendrian contact homology for attaching links in higher dimensional subcritical Weinstein manifolds
• Categorical non-properness in wrapped Floer theory
• Stein domains with exotic contact boundaries
• A note on the representability of a certain Hamiltonian capacity