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Katsuhiko Kuribayashi
The Hochschild cohomology ring of the singular cochain algebra of a space
(L’anneau de cohomologie de Hochschild des cochaînes singulières d’un espace)
Annales de l'institut Fourier, 61 no. 5 (2011), p. 1779-1805, doi: 10.5802/aif.2658
Article PDF | Reviews MR 2961840 | Zbl 1279.16009
Class. Math.: 16E40, 16E45, 55P35
Keywords: Hochschild cohomology, singular cochain algebra, Batalin-Vilkovisky algebra, Koszul-Tate resolution.

Résumé - Abstract

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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