Floer homology and the heat flow

Details Floer homology and the heat flow Floer homology and the heat flow

2003-04-24

arxiv.org/abs/math/0304383v2

Mathematics

Symplectic Geometry

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

Scientific paper

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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