Genus Integration, Abelianization, and Extended Monodromy

Ivan Contreras, Rui Loja Fernandes

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)10798-10840
Number of pages43
JournalInternational Mathematics Research Notices
Issue number14
StatePublished - Jul 1 2021

ASJC Scopus subject areas

  • General Mathematics


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