Guillemin Transform and Toeplitz Representations for Operators on Singular Manifolds

Details Guillemin Transform and Toeplitz Representations for Operators on Singular Manifolds Guillemin Transform and Toeplitz Representations for Operators on Singular Manifolds

2005-03-14

arxiv.org/abs/math/0503267v1

Contemporary Mathematics, 366, 2005, 281-306

Mathematics

Analysis of PDEs

26 pages

Scientific paper

An approach to the construction of index formulas for elliptic operators on singular manifolds is suggested on the basis of K-theory of algebras and cyclic cohomology. The equivalence of Toeplitz and pseudodifferential quantizations, well known in the case of smooth closed manifolds, is extended to the case of manifolds with conical singularities. We describe a general construction that permits one, for a given Toeplitz quantization of a C^*-algebra, to obtain a new equivalent Toeplitz quantization provided that a resolution of the projection determining the original quantization is given.

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