Hochschild cohomology is topological

Let E be an r-connected finite complex of dimension n, where r greater than or equal to 1, and let p be an odd prime number such that rp greater than or equal to n. A theorem of Anick implies that the cochain algebra C*(E; F-p) is equivalent to a commutative cochain algebra A*(E; F-p). We prove that the Hochschild cohomology algebra of A*(E; F-p) is isomorphic as an algebra to the mod-p cohomology algebra of the free loop space on E. (C) 2001 Elsevier Science B.V. All rights reserved.