On the loop homology of complex projective spaces
Bulletin de la Société Mathématique de France, Volume 139 (2011) no. 4, p. 503-518

In this short note we compute the Chas-Sullivan BV-algebra structure on the singular homology of the free loop space of complex projective spaces. We compare this result with computations in Hochschild cohomology.

Sur l'homologie de l'espace des lacets des espaces projectifs complexes résumé : Dans cette note, on calcule l'homologie singulière de l'espace des lacets libres des espaces projectifs complexes munie de la BV-structure de Chas-Sullivan. On compare ces calculs avec ceux effectués en cohomologie de Hochschild.

DOI : https://doi.org/10.24033/bsmf.2616
Classification:  55P50,  55N45,  55P48
Keywords: free loop spaces, Hochschild homology, string topology
@article{BSMF_2011__139_4_503_0,
     author = {Chataur, David and Le Borgne, Jean-Fran\c cois},
     title = {On the loop homology of complex projective spaces},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {139},
     number = {4},
     year = {2011},
     pages = {503-518},
     doi = {10.24033/bsmf.2616},
     zbl = {1238.55004},
     mrnumber = {2869302},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_2011__139_4_503_0}
}
On the loop homology of complex projective spaces. Bulletin de la Société Mathématique de France, Volume 139 (2011) no. 4, pp. 503-518. doi : 10.24033/bsmf.2616. http://www.numdam.org/item/BSMF_2011__139_4_503_0/

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