Rational string topology

Yves Félix; Jean-Claude Thomas; Micheline Vigué-Poirrier

Journal of the European Mathematical Society (2007)

  • Volume: 009, Issue: 1, page 123-156
  • ISSN: 1435-9855

Abstract

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We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a simply connected closed manifold M . We prove that the loop homology of M is isomorphic to the Hochschild cohomology of the cochain algebra C * ( M ) with coefficients in C * ( M ) . Some explicit computations of the loop product and the string bracket are given.

How to cite

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Félix, Yves, Thomas, Jean-Claude, and Vigué-Poirrier, Micheline. "Rational string topology." Journal of the European Mathematical Society 009.1 (2007): 123-156. <http://eudml.org/doc/277192>.

@article{Félix2007,
abstract = {We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a simply connected closed manifold $M$. We prove that the loop homology of $M$ is isomorphic to the Hochschild cohomology of the cochain algebra $C^*(M)$ with coefficients in $C^*(M)$. Some explicit computations of the loop product and the string bracket are given.},
author = {Félix, Yves, Thomas, Jean-Claude, Vigué-Poirrier, Micheline},
journal = {Journal of the European Mathematical Society},
keywords = {string homology; rational homotopy; Hochschild cohomology; free loop space; loop space homology; rational homotopy; Hochschild cohomology; free loop space; string homology},
language = {eng},
number = {1},
pages = {123-156},
publisher = {European Mathematical Society Publishing House},
title = {Rational string topology},
url = {http://eudml.org/doc/277192},
volume = {009},
year = {2007},
}

TY - JOUR
AU - Félix, Yves
AU - Thomas, Jean-Claude
AU - Vigué-Poirrier, Micheline
TI - Rational string topology
JO - Journal of the European Mathematical Society
PY - 2007
PB - European Mathematical Society Publishing House
VL - 009
IS - 1
SP - 123
EP - 156
AB - We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a simply connected closed manifold $M$. We prove that the loop homology of $M$ is isomorphic to the Hochschild cohomology of the cochain algebra $C^*(M)$ with coefficients in $C^*(M)$. Some explicit computations of the loop product and the string bracket are given.
LA - eng
KW - string homology; rational homotopy; Hochschild cohomology; free loop space; loop space homology; rational homotopy; Hochschild cohomology; free loop space; string homology
UR - http://eudml.org/doc/277192
ER -

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