Floer homology and the heat flow

Abstract

We study the heat flow in the loop space of a closed Riemannian manifold $M$ as an adiabatic limit of the Floer equations in the cotangent bundle. Our main application is a proof that the Floer homology of the cotangent bundle, for the Hamiltonian function kinetic plus potential energy, is naturally isomorphic to the homology of the loop space.

83 pages, 1 figure. We introduce a class of abstract perturbations in order to achieve transversality. The argument carries over to this class

References in corpus (3)

• Functors and Computations in Floer homology with Applications Part II
• The Morse-Witten complex via dynamical systems
• Noncontractible periodic orbits in cotangent bundles and Floer homology

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