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 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.
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