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Titlebook: Quantization of Singular Symplectic Quotients; N. P. Landsman,M. Pflaum,M. Schlichenmaier Conference proceedings 2001 Springer Basel AG 20

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Quantized reduction as a tensor product,es of dual pairs, with symplectic groupoids as units. Morita equivalence of Poisson manifolds amounts to isomorphism of objects in this category..This description paves the way for the quantization of the classical reduction procedure, which is based on the formal analogy between dual pairs of Poiss
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Smooth structures on stratified spaces, one needs an appropriate functional structure on these spaces. But unlike for manifolds such a functional structure on a stratified space is in general not intrinsically given. In this article we explain the basic notions of the theory of stratified spaces and define an appropriate concept for a so
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Combinatorial quantization of Euclidean gravity in three dimensions,surface, where . is a typically non-compact Lie group which depends on the signature of space-time and the cosmological constant. For Euclidean signature and vanishing cosmological constant, . is the three-dimensional Euclidean group. For this case the Poisson structure of the moduli space is given
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Homology of complete symbols and noncommutative geometry,(.) 0 ≅ .* (.) × (0, ∞), the dual of.with the zero section removed. We use then these results to compute the Hochschild and cyclic homologies of the algebras of complete symbols associated with manifolds with corners, when the corresponding Lie algebroid is rationally isomorphic to the tangent bundle.
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