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

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

2010-06-04

arxiv.org/abs/1006.0884v4

Mathematics

Algebraic Topology

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

Scientific paper

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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