BV structure on the Hochschild cohomology of Sullivan algebras | Zendy

J.-B. Gatsinzi | Zendy

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BV structure on the Hochschild cohomology of Sullivan algebras

Author(s) -

J.-B. Gatsinzi

Publication year - 2017

Publication title -

journal of the egyptian mathematical society

Language(s) - English

Resource type - Journals

eISSN - 2090-9128

pISSN - 1110-256X

DOI - 10.1016/j.joems.2017.03.001

Subject(s) - mathematics , cohomology , homology (biology) , pure mathematics , loop space , loop (graph theory) , manifold (fluid mechanics) , combinatorics , algebra over a field , mechanical engineering , biochemistry , chemistry , engineering , gene

Let X be a closed, simply connected manifold of dimension m and LX the space of free loops on X. If (∧V, d) is the minimal Sullivan model of X where V is finite dimensional, then there is a Gerstenhaber algebra (∧V⊗∧s−1V#,d0), where V# is the graded dual of V, and its homology is isomorphic to the loop space homology H*(LX). In this paper we define a BV structure on (∧V⊗∧s−1V#,d0) which extends the Gerstenhaber bracket

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