Covariant and Equivariant Formality Theorems

dc.creatorDolgushev, Vasiliy
dc.date2003-07-16
dc.date2003-09-26
dc.date.accessioned2026-07-07T04:59:40Z
dc.date.available2026-07-07T04:59:40Z
dc.descriptionWe 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.description26 pages, no figures
dc.identifierhttps://arxiv.org/abs/math/0307212
dc.identifierhttp://arxiv.org/abs/math/0307212
dc.identifierAdv. Math., Vol. 191, 1 (2005) 147-177
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68081
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectDifferential Geometry
dc.subject16E45; 53C15
dc.titleCovariant and Equivariant Formality Theorems
dc.typetext

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