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.

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: 10.5802/aif.2658
Classification: 16E40,  16E45,  55P35
Keywords: Hochschild cohomology, singular cochain algebra, Batalin-Vilkovisky algebra, Koszul-Tate resolution.
Kuribayashi, Katsuhiko 1

1 Shinshu University, Faculty of Science, Department of Mathematical Sciences, Matsumoto, Nagano 390-8621, Japan
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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. http://archive.numdam.org/articles/10.5802/aif.2658/

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