English

Floer homology and the heat flow

Symplectic Geometry 2014-02-10 v2 Analysis of PDEs Differential Geometry

Abstract

We study the heat flow in the loop space of a closed Riemannian manifold MM 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.

Keywords

Cite

@article{arxiv.math/0304383,
  title  = {Floer homology and the heat flow},
  author = {Dietmar A. Salamon and Joa Weber},
  journal= {arXiv preprint arXiv:math/0304383},
  year   = {2014}
}

Comments

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