The Hochschild cohomology ring of the singular cochain algebra of a space
Annales de l'Institut Fourier, Volume 61 (2011) no. 5, p. 1779-1805
We determine the algebra structure of the Hochschild cohomology of the singular cochain algebra with coefficients in a field on a space whose cohomology is a polynomial algebra. A spectral sequence calculation of the Hochschild cohomology is also described. In particular, when the underlying field is of characteristic two, we determine the associated bigraded Batalin-Vilkovisky algebra structure on the Hochschild cohomology of the singular cochain on a space whose cohomology is an exterior algebra.
Nous déterminons la structure d’algèbre sur la cohomologie de Hochschild des cochaînes singulières à coefficients dans un corps d’un espace dont la cohomologie est une algèbre polynômiale. Un calcul de cohomologie de Hochschild à l’aide d’une suite spectrale est aussi décrit. En particulier, quand le corps sous-jacent est de caractéristique deux, nous déterminons la structure d’algèbre de Batalin-Vilkovisky bigraduée associée à la cohomologie de Hochschild des cochaînes singulières d’un espace dont la cohomologie est une algèbre extérieure.
DOI : https://doi.org/10.5802/aif.2658
Classification:  16E40,  16E45,  55P35
Keywords: Hochschild cohomology, singular cochain algebra, Batalin-Vilkovisky algebra, Koszul-Tate resolution.
@article{AIF_2011__61_5_1779_0,
     author = {Kuribayashi, Katsuhiko},
     title = {The Hochschild cohomology ring of the singular cochain algebra of a space},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {61},
     number = {5},
     year = {2011},
     pages = {1779-1805},
     doi = {10.5802/aif.2658},
     zbl = {1279.16009},
     mrnumber = {2961840},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2011__61_5_1779_0}
}
Kuribayashi, Katsuhiko. The Hochschild cohomology ring of the singular cochain algebra of a space. Annales de l'Institut Fourier, Volume 61 (2011) no. 5, pp. 1779-1805. doi : 10.5802/aif.2658. https://aif.centre-mersenne.org/item/AIF_2011__61_5_1779_0/

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