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

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.

20 pages. Some references are added. The proof of Theorem 4.3 is revised. Final version, to appear in Annales de l'Institut Fourier