# 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

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topFélix, 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 -

## Citations in EuDML Documents

top- Pascal Lambrechts, Don Stanley, Poincaré duality and commutative differential graded algebras
- Yves Félix, Jean-Claude Thomas, Rational BV-algebra in string topology
- Katsuhiko Kuribayashi, The Hochschild cohomology ring of the singular cochain algebra of a space
- Grégory Ginot, Thomas Tradler, Mahmoud Zeinalian, A Chen model for mapping spaces and the surface product

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