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Floer Homology and the Heat Flow

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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.

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Authors and Affiliations

  1. ETH-Zürich, Rämistrasse 101, CH-8092, Zürich, Switzerland

    D. A. Salamon & J. Weber

  2. Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099, Berlin, Germany

    D. A. Salamon

Authors
  1. D. A. Salamon
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  2. J. Weber
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Corresponding author

Correspondence to D. A. Salamon.

Additional information

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). https://doi.org/10.1007/s00039-006-0577-4

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  • DOI: https://doi.org/10.1007/s00039-006-0577-4

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