A Morse theoretic description of string topology

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

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Geometric Topology, 57R19; 58E05; 57R58

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http://salesiana.dossiersoluciones.com/handle/123456789/171689

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0809.0868
 http://arxiv.org/abs/0809.0868

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arXiv