Théorème de formalité pour les g-variétés

Translated title of the contribution: Formality theorem for g-manifolds

Hsuan Yi Liao, Mathieu Stiénon, Ping Xu

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

With any g-manifold M are associated two dglas tot(ΛgkTpoly(M)) and tot(ΛgkDpoly(M)), whose cohomologies HCE(g,Tpoly(M)→0Tpoly•+1(M)) and HCE(g,Dpoly(M)→dHDpoly•+1(M)) are Gerstenhaber algebras. We establish a formality theorem for g-manifolds: there exists an L quasi-isomorphism Φ:tot(ΛgkTpoly(M))→tot(ΛgkDpoly(M)) whose first ‘Taylor coefficient’ (1) is equal to the Hochschild–Kostant–Rosenberg map twisted by the square root of the Todd cocycle of the g-manifold M, and (2) induces an isomorphism of Gerstenhaber algebras on the level of cohomology. Consequently, the Hochschild–Kostant–Rosenberg map twisted by the square root of the Todd class of the g-manifold M is an isomorphism of Gerstenhaber algebras from HCE(g,Tpoly(M)→0Tpoly•+1(M)) to HCE(g,Dpoly(M)→dHDpoly•+1(M)).

Translated title of the contributionFormality theorem for g-manifolds
Original languageFrench
Pages (from-to)582-589
Number of pages8
JournalComptes Rendus Mathematique
Volume355
Issue number5
DOIs
StatePublished - May 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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