Integrability of Jacobi and Poisson structures

Marius Crainic[1]; Chenchang Zhu[2]

  • [1] Utrecht University Department of Mathematics 3508 TA Utrecht (The Netherlands)
  • [2] University of California Department of Mathematics Berkeley, CA 94720 (U.S.A.)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 4, page 1181-1216
  • ISSN: 0373-0956

Abstract

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We discuss the integrability of Jacobi manifolds by contact groupoids, and then look at what the Jacobi point of view brings new into Poisson geometry. In particular, using contact groupoids, we prove a Kostant-type theorem on the prequantization of symplectic groupoids, which answers a question posed by Weinstein and Xu. The methods used are those of Crainic-Fernandes on A -paths and monodromy group(oid)s of algebroids. In particular, most of the results we obtain are valid also in the non-integrable case.

How to cite

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Crainic, Marius, and Zhu, Chenchang. "Integrability of Jacobi and Poisson structures." Annales de l’institut Fourier 57.4 (2007): 1181-1216. <http://eudml.org/doc/10255>.

@article{Crainic2007,
abstract = {We discuss the integrability of Jacobi manifolds by contact groupoids, and then look at what the Jacobi point of view brings new into Poisson geometry. In particular, using contact groupoids, we prove a Kostant-type theorem on the prequantization of symplectic groupoids, which answers a question posed by Weinstein and Xu. The methods used are those of Crainic-Fernandes on $A$-paths and monodromy group(oid)s of algebroids. In particular, most of the results we obtain are valid also in the non-integrable case.},
affiliation = {Utrecht University Department of Mathematics 3508 TA Utrecht (The Netherlands); University of California Department of Mathematics Berkeley, CA 94720 (U.S.A.)},
author = {Crainic, Marius, Zhu, Chenchang},
journal = {Annales de l’institut Fourier},
keywords = {Jacobi structure; Poisson geometry; prequantization; contact groupoids; integration},
language = {eng},
number = {4},
pages = {1181-1216},
publisher = {Association des Annales de l’institut Fourier},
title = {Integrability of Jacobi and Poisson structures},
url = {http://eudml.org/doc/10255},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Crainic, Marius
AU - Zhu, Chenchang
TI - Integrability of Jacobi and Poisson structures
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 4
SP - 1181
EP - 1216
AB - We discuss the integrability of Jacobi manifolds by contact groupoids, and then look at what the Jacobi point of view brings new into Poisson geometry. In particular, using contact groupoids, we prove a Kostant-type theorem on the prequantization of symplectic groupoids, which answers a question posed by Weinstein and Xu. The methods used are those of Crainic-Fernandes on $A$-paths and monodromy group(oid)s of algebroids. In particular, most of the results we obtain are valid also in the non-integrable case.
LA - eng
KW - Jacobi structure; Poisson geometry; prequantization; contact groupoids; integration
UR - http://eudml.org/doc/10255
ER -

References

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