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Creators/Authors contains: "Contreras, Ivan"

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  1. ; ; ; ; (, Linear and Multilinear Algebra)
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  2. ; ; (, Letters in Mathematical Physics)
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  3. ; (, International Mathematics Research Notices)
    Abstract Given a Lie algebroid we discuss the existence of a smooth abelian integration of its abelianization. We show that the obstructions are related to the extended monodromy groups introduced recently in [9]. We also show that this groupoid can be obtained by a path-space construction, similar to the Weinstein groupoid of [6], but where the underlying homotopies are now supported in surfaces with arbitrary genus. As an application, we show that the prequantization condition for a (possibly non-simply connected) manifold is equivalent to the smoothness of an abelian integration. Our results can be interpreted as a generalization of the classical Hurewicz theorem. 
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