Gauge equivalence of Dirac structures and symplectic groupoids

Henrique Bursztyn[1]; Olga Radko[2]

  • [1] University of Toronto, Department of Mathematics, Toronto, Ontario M5S 3G3 (Canada)
  • [2] University of California, Department of Mathematics, Berkeley CA 94720 (USA)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 1, page 309-337
  • ISSN: 0373-0956

Abstract

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We study gauge transformations of Dirac structures and the relationship between gauge and Morita equivalences of Poisson manifolds. We describe how the symplectic structure of a symplectic groupoid is affected by a gauge transformation of the Poisson structure on its identity section, and prove that gauge-equivalent integrable Poisson structures are Morita equivalent. As an example, we study certain generic sets of Poisson structures on Riemann surfaces: we find complete gauge-equivalence invariants for such structures which, on the 2 -sphere, yield a complete invariant of Morita equivalence.

How to cite

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Bursztyn, Henrique, and Radko, Olga. "Gauge equivalence of Dirac structures and symplectic groupoids." Annales de l’institut Fourier 53.1 (2003): 309-337. <http://eudml.org/doc/116037>.

@article{Bursztyn2003,
abstract = {We study gauge transformations of Dirac structures and the relationship between gauge and Morita equivalences of Poisson manifolds. We describe how the symplectic structure of a symplectic groupoid is affected by a gauge transformation of the Poisson structure on its identity section, and prove that gauge-equivalent integrable Poisson structures are Morita equivalent. As an example, we study certain generic sets of Poisson structures on Riemann surfaces: we find complete gauge-equivalence invariants for such structures which, on the $2$-sphere, yield a complete invariant of Morita equivalence.},
affiliation = {University of Toronto, Department of Mathematics, Toronto, Ontario M5S 3G3 (Canada); University of California, Department of Mathematics, Berkeley CA 94720 (USA)},
author = {Bursztyn, Henrique, Radko, Olga},
journal = {Annales de l’institut Fourier},
keywords = {Dirac structures; gauge equivalence; Morita equivalence; symplectic groupoids},
language = {eng},
number = {1},
pages = {309-337},
publisher = {Association des Annales de l'Institut Fourier},
title = {Gauge equivalence of Dirac structures and symplectic groupoids},
url = {http://eudml.org/doc/116037},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Bursztyn, Henrique
AU - Radko, Olga
TI - Gauge equivalence of Dirac structures and symplectic groupoids
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 1
SP - 309
EP - 337
AB - We study gauge transformations of Dirac structures and the relationship between gauge and Morita equivalences of Poisson manifolds. We describe how the symplectic structure of a symplectic groupoid is affected by a gauge transformation of the Poisson structure on its identity section, and prove that gauge-equivalent integrable Poisson structures are Morita equivalent. As an example, we study certain generic sets of Poisson structures on Riemann surfaces: we find complete gauge-equivalence invariants for such structures which, on the $2$-sphere, yield a complete invariant of Morita equivalence.
LA - eng
KW - Dirac structures; gauge equivalence; Morita equivalence; symplectic groupoids
UR - http://eudml.org/doc/116037
ER -

References

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