Titlebook: Loop Spaces, Characteristic Classes and Geometric Quantization; Jean-Luc Brylinski Textbook 1993 Birkhäuser Boston 1993 Algebra.Category t

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Line Bundles and Central Extensions,n sections of the line bundle (Kostant). A similar central extension exists in a holomorphic context (Mumford). In §2.5, we discuss results of Weinstein, which give a similar central extension when there is no line bundle (because the given 2-form is not integral).

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Degree 3 Cohomology: Sheaves of Groupoids,his to the constructions of Chapter 4. In §4 we use the path-fibration to define a canonical sheaf of groupoids over a compact Lie group. In §5 we give other examples of sheaves of groupoids connected with Lie group actions on a smooth manifold and with sheaves of twisted differential operators.

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