Functors and Computations in Floer homology with Applications Part II

TL;DR

This paper establishes isomorphisms between Floer cohomology, generating function cohomology, and loop space cohomology, providing new computational tools and insights in symplectic topology.

Contribution

It proves the equivalence of Floer cohomology with generating function cohomology and relates Floer cohomology of cotangent bundles to loop space cohomology, extending previous results.

Findings

Floer cohomology is isomorphic to generating function cohomology

Floer cohomology of cotangent bundles equals loop space cohomology

Provides computational methods for Floer cohomology

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{\"u}rich. Up to typos, this is the revised version from 2003.