English

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].

Keywords

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

R2 v1 2026-06-21T22:35:40.076Z