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.
Original language | English (US) |
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Pages (from-to) | 10798-10840 |
Number of pages | 43 |
Journal | International Mathematics Research Notices |
Volume | 2021 |
Issue number | 14 |
DOIs | |
State | Published - Jul 1 2021 |
ASJC Scopus subject areas
- General Mathematics