Floer Homology and the Heat Flow

2003/04/30 by Dietmar Salamon, Dietmar A. Salamon, Joa Weber · 4 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AP #math.DG #math.SG #msc:35J60 #msc:35K55 #msc:53D40 #msc:57R58 #msc:58B05

paper · pdf · doi:10.1007/s00039-006-0577-4

published as GAFA 16 no.5 (2006), 1050--1138 · 83 pages, 1 figure. We introduce a class of abstract perturbations in order to achieve transversality. The argument carries over to this class

arxiv created 2004/09/29 · openalex publication_date 2006/10/03 · arxiv updated 2014/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Perturbed closed geodesics are periodic orbits: Index and transversality
• Self-Dual Instantons and Holomorphic Curves
• Morse theory for periodic solutions of hamiltonian systems and the maslov index
• Functors and Computations in Floer homology with Applications Part II

Cited by

• The Arnol'd chord conjecture for ST^*T³
• Braid Floer homology
• Noncontractible periodic orbits in cotangent bundles and Floer homology
• Geometry of contact transformations and domains: orderability versus squeezing