Poincaré duality and commutative differential graded algebras
Annales scientifiques de l'École Normale Supérieure, Série 4, Volume 41 (2008) no. 4, p. 497-511
We prove that every commutative differential graded algebra whose cohomology is a simply-connected Poincaré duality algebra is quasi-isomorphic to one whose underlying algebra is simply-connected and satisfies Poincaré duality in the same dimension. This has applications in rational homotopy, giving Poincaré duality at the cochain level, which is of interest in particular in the study of configuration spaces and in string topology.
Nous démontrons que toute algèbre différentielle graduée commutative (ADGC) dont la cohomologie est une algèbre simplement connexe à dualité de Poincaré est quasi-isomorphe à une ADGC dont l'algèbre sous-jacente est à dualité de Poincaré dans la même dimension. Ce résultat a des applications en théorie de l'homotopie rationnelle, permettant d'obtenir la dualité de Poincaré au niveau des cochaînes, entre autres dans l'étude des espaces de configurations et en topologie des cordes.
DOI : https://doi.org/10.24033/asens.2074
Classification:  55P62,  55M05,  57P10
Keywords: poincaré duality, commutative differential graded algebra
@article{ASENS_2008_4_41_4_497_0,
     author = {Lambrechts, Pascal and Stanley, Don},
     title = {Poincar\'e duality and commutative differential graded algebras},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 41},
     number = {4},
     year = {2008},
     pages = {497-511},
     doi = {10.24033/asens.2074},
     zbl = {1172.13009},
     mrnumber = {2489632},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2008_4_41_4_497_0}
}
Lambrechts, Pascal; Stanley, Don. Poincaré duality and commutative differential graded algebras. Annales scientifiques de l'École Normale Supérieure, Série 4, Volume 41 (2008) no. 4, pp. 497-511. doi : 10.24033/asens.2074. http://www.numdam.org/item/ASENS_2008_4_41_4_497_0/

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