Associativity and integrability
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- by Rui Loja Fernandes and Daan Michiels PDF
- Trans. Amer. Math. Soc. 373 (2020), 5057-5110 Request permission
Abstract:
We provide a complete solution to the problem of extending a local Lie groupoid to a global Lie groupoid. First, we show that the classical Mal’cev’s theorem, which characterizes local Lie groups that can be extended to global Lie groups, also holds in the groupoid setting. Next, we describe a construction that can be used to obtain any local Lie groupoid with integrable algebroid. Last, our main result establishes a precise relationship between the integrability of a Lie algebroid and the failure in associativity of a local integration. We give a simplicial interpretation of this result showing that the monodromy groups of a Lie algebroid manifest themselves combinatorially in a local integration, as a lack of associativity.References
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Additional Information
- Rui Loja Fernandes
- Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801
- MR Author ID: 341522
- Email: ruiloja@illinois.edu
- Daan Michiels
- Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801
- Received by editor(s): June 20, 2019
- Received by editor(s) in revised form: November 24, 2019
- Published electronically: April 28, 2020
- Additional Notes: This work was partially supported by NSF grants DMS 13-08472, DMS 14-05671, DMS-1710884, and FCT/Portugal.
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 5057-5110
- MSC (2010): Primary 58H05; Secondary 22A22, 22E05, 53D17
- DOI: https://doi.org/10.1090/tran/8073
- MathSciNet review: 4127871