Translator Disclaimer
15 June 2004 Integration of twisted Dirac brackets
Henrique Bursztyn, Marius Crainic, Alan Weinstein, Chenchang Zhu
Duke Math. J. 123(3): 549-607 (15 June 2004). DOI: 10.1215/S0012-7094-04-12335-8

Abstract

Given a Lie groupoid G over a manifold M, we show that multiplicative 2-forms on G relatively closed with respect to a closed 3-form ϕ; on M correspond to maps from the Lie algebroid of G into T*M satisfying an algebraic condition and a differential condition with respect to the ϕ-twisted Courant bracket. This correspondence describes, as a special case, the global objects associated to ϕ-twisted Dirac structures. As applications, we relate our results to equivariant cohomology and foliation theory, and we give a new description of quasi-Hamiltonian spaces and group-valued momentum maps.

Citation

Download Citation

Henrique Bursztyn. Marius Crainic. Alan Weinstein. Chenchang Zhu. "Integration of twisted Dirac brackets." Duke Math. J. 123 (3) 549 - 607, 15 June 2004. https://doi.org/10.1215/S0012-7094-04-12335-8

Information

Published: 15 June 2004
First available in Project Euclid: 11 June 2004

zbMATH: 1067.58016
MathSciNet: MR2068969
Digital Object Identifier: 10.1215/S0012-7094-04-12335-8

Subjects:
Primary: 58H05
Secondary: 53C12, 53D17, 53D20

Rights: Copyright © 2004 Duke University Press

JOURNAL ARTICLE
59 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.123 • No. 3 • 15 June 2004
Back to Top