Mathematics – Algebraic Geometry
Scientific paper
2009-04-30
Mathematics
Algebraic Geometry
48 pages, 2 figures; a number of additional explanations added (suggested by the referees)
Scientific paper
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.
Calaque Damien
den Bergh Michel Van
Rossi Carlo A.
No associations
LandOfFree
Caldararu's conjecture and Tsygan's formality does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Caldararu's conjecture and Tsygan's formality, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Caldararu's conjecture and Tsygan's formality will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-443892