Videos

Floer Homology and Loop Space Topology

Presenter
November 4, 2011
Keywords:
  • Shiing-Shen Chern
  • differential geometry
  • loop space
  • Floer homology
  • symplectic geometry
  • surgery theory
  • Morse theory and mathematical physics
MSC:
  • 53-xx
  • 53D40
  • 53D42
  • 53Dxx
  • 37B30
  • 55P35
  • 55Pxx
  • 55-xx
Abstract
Floer homology for Hamiltonian systems can be viewed as infinite dimensional Morse homology on loop spaces. Whereas, on closed symplectic manifolds, Floer homology turns out to be finite-dimensional, on noncompact spaces it can be infinite-dimensional. In fact, on cotangent bundles, Floer homology is isomorphic to the loop space homology. This isomorphism extends also to the naturally defined product structures, the pair-of-pants product.