Duality in Gerstenhaber algebras

Details Duality in Gerstenhaber algebras Duality in Gerstenhaber algebras

2002-11-14

arxiv.org/abs/math/0211229v1

Mathematics

Algebraic Topology

21 Pages

Scientific paper

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 $HH^\ast (C^\vee, C ^\vee)$ and $HH^\ast (\bar\Omega C ; \bar\Omega C)$. 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.

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