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Floer Homology and the Heat Flow

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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.

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Correspondence to D. A. Salamon.

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J.W. received partial financial support from TH-Projekt 00321.

Received: December 2004 Revision: September 2005 Accepted: September 2005

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Salamon, D.A., Weber, J. Floer Homology and the Heat Flow. GAFA, Geom. funct. anal. 16, 1050–1138 (2006).

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