The backward {\lambda}-Lemma and Morse filtrations
Dynamical Systems
2017-09-25 v2 Analysis of PDEs
Algebraic Topology
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 {\lambda}-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].
Cite
@article{arxiv.1211.2180,
title = {The backward {\lambda}-Lemma and Morse filtrations},
author = {Joa Weber},
journal= {arXiv preprint arXiv:1211.2180},
year = {2017}
}
Comments
Conference proceedings, 9 pages, 5 figures. v2: typos corrected, minor modifications