Théorème de formalité pour les variétés différentielles graduées

Translated title of the contribution: Formality theorem for differential graded manifolds

Hsuan Yi Liao, Mathieu Stiénon, Ping Xu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We establish a formality theorem for smooth dg manifolds. More precisely, we prove that, for any finite-dimensional dg manifold (M,Q), there exists an L quasi-isomorphism of dglas from (Tpoly•⊕(M),[Q,−],[−,−]) to (Dpoly•⊕(M),〚m+Q,−〛,〚−,−〛) whose first Taylor coefficient (1) is equal to the composition hkr∘(td(M,Q) )1/2:Tpoly•⊕(M)→Dpoly•⊕(M) of the action of (td(M,Q) )1/2∈∏k≥0k(M))k on Tpoly•⊕(M) (by contraction) with the Hochschild–Kostant–Rosenberg map and (2) preserves the associative algebra structures on the level of cohomology. As an application, we prove the Kontsevich–Shoikhet conjecture: a Kontsevich–Duflo-type theorem holds for all finite-dimensional smooth dg manifolds.

Translated title of the contributionFormality theorem for differential graded manifolds
Original languageFrench
Pages (from-to)27-43
Number of pages17
JournalComptes Rendus Mathematique
Volume356
Issue number1
DOIs
StatePublished - Jan 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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