A Morse theoretic description of string topology

Details A Morse theoretic description of string topology A Morse theoretic description of string topology

2008-09-04

arxiv.org/abs/0809.0868v2

Mathematics

Geometric Topology

30 pages, 6 figures Final version to appear in Proc. of Conference on Symplectic Field Theory in honor of the 60th birthday of

Scientific paper

Let M be a closed, oriented, n-dimensional manifold. In this paper we give a Morse theoretic description of the string topology operations introduced by Chas and Sullivan, and extended by the first author, Jones, Godin, and others. We do this by studying maps from surfaces with cylindrical ends to M, such that on the cylinders, they satisfy the gradient flow equation of a Morse function on the loop space, LM. We then give Morse theoretic descriptions of related constructions, such as the Thom and Euler classes of a vector bundle, as well as the shriek, or unkehr homomorphism.

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