Morse homology for the heat flow

Details Morse homology for the heat flow Morse homology for the heat flow

2010-03-23

arxiv.org/abs/1003.4350v1

Mathematics

Differential Geometry

89 pages, 3 figures

Scientific paper

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.

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