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Journal Articles Letters in Mathematical Physics Year : 2011

Compatibility with cap-products in Tsygan's formality and homological Duflo isomorphism

Abstract

In this paper we prove that the isomorphism induced on tangent homology by the Shoikhet-Tsygan formality isomorphism for Hochschild chains is compatible with cap-products. This is a homological analog of the compatibility with cup-products of the isomorphism induced on tangent cohomology by Kontsevich formality isomorphism for Hochschild cochains. As in the cohomological situation our proof relies on a homotopy argument. This homotopy argument involves a 2-dimensional surface in a 3-dimensional configuration space, the {\bf I-cube} (which plays the rôle of {\bf Kontsevich's eye}). As an application, we state and prove a homological version of the Duflo isomorphism.

Dates and versions

hal-00281612 , version 1 (23-05-2008)

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Cite

Damien Calaque, Carlo A. Rossi. Compatibility with cap-products in Tsygan's formality and homological Duflo isomorphism. Letters in Mathematical Physics, 2011, 95 (2), pp.135-209. ⟨10.1007/s11005-010-0451-z⟩. ⟨hal-00281612⟩
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