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.