Let M be a closed orientable manifold of dimension and be the usual cochain algebra on M with coefficients in a field . The Hochschild cohomology of M, is a graded commutative and associative algebra. The augmentation map induces a morphism of algebras . In this paper we produce a chain model for the morphism I. We show that the kernel of I is a nilpotent ideal and that the image of I is contained in the center of , which is in general quite small. The algebra is expected to be isomorphic to the loop homology constructed by Chas and Sullivan. Thus our results would be translated in terms of string homology.
@article{PMIHES_2004__99__235_0, author = {Felix, Yves and Thomas, Jean-Claude and Vigu\'e-Poirrier, Micheline}, title = {The {Hochschild} cohomology of a closed manifold}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {235--252}, publisher = {Springer}, volume = {99}, year = {2004}, doi = {10.1007/s10240-004-0021-y}, mrnumber = {2075886}, zbl = {1060.57019}, language = {en}, url = {http://www.numdam.org/articles/10.1007/s10240-004-0021-y/} }
TY - JOUR AU - Felix, Yves AU - Thomas, Jean-Claude AU - Vigué-Poirrier, Micheline TI - The Hochschild cohomology of a closed manifold JO - Publications Mathématiques de l'IHÉS PY - 2004 SP - 235 EP - 252 VL - 99 PB - Springer UR - http://www.numdam.org/articles/10.1007/s10240-004-0021-y/ DO - 10.1007/s10240-004-0021-y LA - en ID - PMIHES_2004__99__235_0 ER -
%0 Journal Article %A Felix, Yves %A Thomas, Jean-Claude %A Vigué-Poirrier, Micheline %T The Hochschild cohomology of a closed manifold %J Publications Mathématiques de l'IHÉS %D 2004 %P 235-252 %V 99 %I Springer %U http://www.numdam.org/articles/10.1007/s10240-004-0021-y/ %R 10.1007/s10240-004-0021-y %G en %F PMIHES_2004__99__235_0
Felix, Yves; Thomas, Jean-Claude; Vigué-Poirrier, Micheline. The Hochschild cohomology of a closed manifold. Publications Mathématiques de l'IHÉS, Tome 99 (2004), pp. 235-252. doi : 10.1007/s10240-004-0021-y. http://www.numdam.org/articles/10.1007/s10240-004-0021-y/
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