Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/14299
Title: Caldararu's conjecture and Tsygan's formality
Authors: Calaque, Damien
Rossi, Carlo A.
VAN DEN BERGH, Michel 
Issue Date: 2012
Publisher: ANNAL MATHEMATICS
Source: ANNALS OF MATHEMATICS, 176 (2), p. 865-923
Abstract: In this paper we complete the proof of Caldararu's conjecture on the compatibility between the module structures on differential forms over polyvector fields and on Hochschild homology over Hochschild cohomology. In fact we show that twisting with the square root of the Todd class gives an isomorphism of precalculi between these pairs of objects. Our methods use formal geometry to globalize the local formality quasi-isomorphisms introduced by Kontsevich and Shoikhet. (The existence of the latter was conjectured by Tsygan.) We also rely on the fact - recently proved by the first two authors - that Shoikhet's quasi-isomorphism is compatible with cap products after twisting with a Maurer-Cartan element.
Notes: [Calaque, Damien] ETH, Zurich, Switzerland. [Calaque, Damien] CNRS, Inst Camille Jordan, F-75700 Paris, France. [Calaque, Damien] Univ Lyon 1, F-69622 Villeurbanne, France. [Rossi, Carlo A.] MPIM Bonn, Bonn, Germany. [Van den Bergh, Michel] Hasselt Univ, Diepenbeek, Belgium.
Keywords: Mathematics; Caldararu's conjecture; Tsygan formality
Document URI: http://hdl.handle.net/1942/14299
ISSN: 0003-486X
e-ISSN: 1939-8980
DOI: 10.4007/annals.2012.176.2.4
ISI #: 000307878000004
Category: A1
Type: Journal Contribution
Validations: ecoom 2013
Appears in Collections:Research publications

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