The Hochschild cohomology ring of the singular cochain algebra of a space

Kuribayashi, Katsuhiko

Annales de l'Institut Fourier, Tome 61 (2011) no. 5, pp. 1779-1805.

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.

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.

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