Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Associativity and integrability


Authors: Rui Loja Fernandes and Daan Michiels
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
Published electronically: April 28, 2020
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 58H05, 22A22, 22E05, 53D17

Retrieve articles in all journals with MSC (2010): 58H05, 22A22, 22E05, 53D17


Additional Information

Rui Loja Fernandes
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801
Email: ruiloja@illinois.edu

Daan Michiels
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801

DOI: https://doi.org/10.1090/tran/8073
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.
Article copyright: © Copyright 2020 American Mathematical Society