The backward λ-Lemma and Morse filtrations
arXiv:1211.2180 · doi:10.1007/978-3-319-04214-5_27
Abstract
Consider the infinite dimensional hyperbolic dynamical system provided by the (forward) heat semi-flow on the loop space of a closed Riemannian manifold M. We use the recently discovered backward λ-Lemma and elements of Conley theory to construct a Morse filtration of the loop space whose cellular filtration complex represents the Morse complex associated to the downward L2-gradient of the classical action functional. This paper is a survey. Details and proofs will be given in [6].
Conference proceedings, 9 pages, 5 figures. v2: typos corrected, minor modifications