Duality in Gerstenhaber algebras

Abstract

Let $C$ be a differential graded coalgebra, $\bar{\Omega }C$ the Adams cobar construction and $C^{\vee }$ the dual algebra. We prove that for a large class of coalgebras $C$ there is a natural isomorphism of Gerstenhaber algebras between the Hochschild cohomologies $H{H}^{\ast }(C^{\vee },C^{\vee })$ and $H{H}^{\ast }(\bar{\Omega }C;\bar{\Omega }C)$. This result permits to describe a Hodge decomposition of the loop space homology of a closed oriented manifold, in the sense of Chas-Sullivan, when the field of coefficients is of characteristic zero.

21 Pages

Cited by in corpus (2)

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