Covariant and Equivariant Formality Theorems
| dc.creator | Dolgushev, Vasiliy | |
| dc.date | 2003-07-16 | |
| dc.date | 2003-09-26 | |
| dc.date.accessioned | 2026-07-07T04:59:40Z | |
| dc.date.available | 2026-07-07T04:59:40Z | |
| dc.description | We give a proof of Kontsevich's formality theorem for a general manifold using Fedosov resolutions of algebras of polydifferential operators and polyvector fields. The main advantage of our construction of the formality quasi-isomorphism is that it is based on the use of covariant tensors unlike Kontsevich's original proof, which is based on $\infty$-jets of polydifferential operators and polyvector fields. Using our construction we prove that if a group G acts smoothly on a manifold M and M admits a G-invariant affine connection then there exists a G-equivariant quasi-isomorphism of formality. This result implies that if a manifold M is equipped with a smooth action of a finite or compact group G or equipped with a free action of a Lie group G then M admits a G-equivariant formality quasi-isomorphism. In particular, this gives a solution of the deformation quantization problem for an arbitrary Poisson orbifold. | |
| dc.description | 26 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0307212 | |
| dc.identifier | http://arxiv.org/abs/math/0307212 | |
| dc.identifier | Adv. Math., Vol. 191, 1 (2005) 147-177 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68081 | |
| dc.subject | Quantum Algebra | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Differential Geometry | |
| dc.subject | 16E45; 53C15 | |
| dc.title | Covariant and Equivariant Formality Theorems | |
| dc.type | text |