Vol. 278, No. 2, 2015

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Integration of coupling Dirac structures

Olivier Brahic and Rui Loja Fernandes

Vol. 278 (2015), No. 2, 325–367
Abstract

Coupling Dirac structures are Dirac structures defined on the total space of a fibration, generalizing hamiltonian fibrations from symplectic geometry, where one replaces the symplectic structure on the fibers by a Poisson structure. We study the associated Poisson gauge theory, in order to describe the presymplectic groupoid integrating coupling Dirac structures. We find the obstructions to integrability, and we give explicit geometric descriptions of the integration.

Keywords
Dirac structure, coupling, presymplectic integration
Mathematical Subject Classification 2010
Primary: 53D17, 58H05
Milestones
Received: 6 October 2014
Revised: 26 March 2015
Accepted: 20 April 2015
Published: 6 October 2015
Authors
Olivier Brahic
Department of Mathematics
Federal University of Paraná
CP 19081
81531-980 Curitiba-PR
Brazil
Rui Loja Fernandes
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, IL 61801
United States