منابع مشابه
On Kontsevich's Formality Theorem
This paper is submitted as a dissertation for the degree of a Master of Science in Mathematics. It reviews the link between formal deformation quantizations and Poisson manifolds, which was conjectured in 1993. This link is a corollary of a more general statement called "Formality Theorem", proved by Maxim Kontsevich in 1997. supervised by Prof. John Jones
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The use of bundle gerbes and bundle gerbe modules is considered as a replacement for the usual theory of Clifford modules on manifolds that fail to be spin. It is shown that both sides of the Atiyah-Singer index formula for coupled Dirac operators can be given natural interpretations using this language and that the resulting formula is still an identity.
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We prove a relative version of Kontsevich’s formality theorem. This theorem involves a manifold M and a submanifold C and reduces to Kontsevich’s theorem if C=M. It states that the DGLA of multivector fields on an infinitesimal neighbourhood of C is L∞-quasiisomorphic to the DGLA of multidifferential operators acting on sections of the exterior algebra of the conormal bundle. Applications to th...
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We discuss the differential graded Lie algebra (DGLA) of Drinfeld modeled on the tensor algebra ⊗ Ug of the universal enveloping algebra of a Lie algebra g over any field K of characteristic zero. We explicitly analyze the first obstruction to the existence of the formality quasi-isomorphism for this DGLA. Our analysis implies the formality of the DGLA ⊗ Ub of Drinfeld associated to the twodime...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2015
ISSN: 0001-8708
DOI: 10.1016/j.aim.2014.11.025