HAL : hal-00382438, version 1

arXiv : 0904.4890

Fiche détaillée

Récupérer au format BibTeX - EndNote - TEI - RefWorks -

Caldararu's conjecture and Tsygan's formality

Damien Calaque 1, Carlo A. Rossi 2, Michel Van den Bergh

(30/04/2009)

In this paper we complete the proof of Caldararu's conjecture on the compatibility between the module structures on differential forms over poly-vector 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 product after twisting with a Maurer-Cartan element.

1 :	Institut Camille Jordan (ICJ)
	CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon
2 :	ETH D-MATH (ETH)
	Swiss Federal Institute of Technology Zurich

Domaine

:

Mathématiques/Géométrie algébrique Mathématiques/K-théorie et homologie

hal-00382438, version 1

http://hal.archives-ouvertes.fr/hal-00382438

oai:hal.archives-ouvertes.fr:hal-00382438

Contributeur : Damien Calaque <>

Soumis le : Jeudi 7 Mai 2009, 18:06:49

Dernière modification le : Jeudi 10 Septembre 2009, 12:19:02