Morse homology for the heat flow

Abstract

We use the heat flow on the loop space of a closed Riemannian manifold to construct an algebraic chain complex. The chain groups are generated by perturbed closed geodesics. The boundary operator is defined in the spirit of Floer theory by counting, modulo time shift, heat flow trajectories that converge asymptotically to nondegenerate closed geodesics of Morse index difference one.

89 pages, 3 figures

References in corpus (1)

• Floer homology and the heat flow

Cited by in corpus (5)

• Symplectic Tate homology
• Bifurcation of Solutions to the Allen-Cahn Equation
• A backward $\lambda$-Lemma for the forward heat flow
• Contraction method and Lambda-Lemma
• The backward λ-Lemma and Morse filtrations