Geodesic
Rational string topology
Journal of the European Mathematical Society, Tome 9 (2007) no. 1, pp. 123-156

Voir la notice de l'article provenant de la source EMS Press

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 1-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 itself. Some explicit computations of the loop product and the string bracket are given.
DOI : 10.4171/jems/75
Classification : 55-XX, 17-XX, 54-XX, 81-XX
Keywords: String homology, rational homotopy, Hochschild cohomology, free loop space, loop space homology 
@article{JEMS_2007_9_1_a5,
     author = {Yves F\'elix and Jean-Claude Thomas and Micheline Vigu\'e-Poirrier},
     title = {Rational string topology},
     journal = {Journal of the European Mathematical Society},
     pages = {123--156},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2007},
     doi = {10.4171/jems/75},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/75/}
}
TY  - JOUR
AU  - Yves Félix
AU  - Jean-Claude Thomas
AU  - Micheline Vigué-Poirrier
TI  - Rational string topology
JO  - Journal of the European Mathematical Society
PY  - 2007
SP  - 123
EP  - 156
VL  - 9
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/75/
DO  - 10.4171/jems/75
ID  - JEMS_2007_9_1_a5
ER  - 
%0 Journal Article
%A Yves Félix
%A Jean-Claude Thomas
%A Micheline Vigué-Poirrier
%T Rational string topology
%J Journal of the European Mathematical Society
%D 2007
%P 123-156
%V 9
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/75/
%R 10.4171/jems/75
%F JEMS_2007_9_1_a5
Yves Félix; Jean-Claude Thomas; Micheline Vigué-Poirrier. Rational string topology. Journal of the European Mathematical Society, Tome 9 (2007) no. 1, pp. 123-156. doi: 10.4171/jems/75

Cité par Sources :