On Kontsevich's Hochschild cohomology conjecture

Details On Kontsevich's Hochschild cohomology conjecture On Kontsevich's Hochschild cohomology conjecture

2003-09-22

arxiv.org/abs/math/0309369v2

Mathematics

Algebraic Topology

29 pages; final version, to appear in Compos. Math

Scientific paper

Let an n-algebra mean an algebra over the chain complex of the little n-cubes
operad. We give a proof of Kontsevich's conjecture, which states that for a
suitable notion of Hochschild cohomology in the category of n-algebras, the
Hochschild cohomology complex of an n-algebra is an (n+1)-algebra. This
generalizes a conjecture by Deligne for n=1, now proven by several authors.

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