September  2012, 4(3): 313-332. doi: 10.3934/jgm.2012.4.313

The leaf space of a multiplicative foliation

1. 

Section de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland

Received  November 2010 Revised  October 2011 Published  October 2012

We show that if a smooth multiplicative subbundle $S\subseteq TG$ on a groupoid $G⇉P$ is involutive and satisfies completeness conditions, then its leaf space $G/S$ inherits a groupoid structure over the space of leaves of $TP\cap S$ in $P$.
    As an application, a special class of Dirac groupoids is shown to project by forward Dirac maps to Poisson groupoids.
Citation: M. Jotz. The leaf space of a multiplicative foliation. Journal of Geometric Mechanics, 2012, 4 (3) : 313-332. doi: 10.3934/jgm.2012.4.313
References:
[1]

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Ph. D. thesis, Instituto de Matemática Pura e Aplicada, 2009. Google Scholar

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Proc. London Math. Soc. (3), 29 (1974), 699-713. doi: 10.1112/plms/s3-29.4.699.  Google Scholar

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J. London Math. Soc. (2), 21 (1980), 544-556.  Google Scholar

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show all references

References:
[1]

Publications du Département de Mathématiques. Nouvelle Série. A, 2, Publ. Dép. Math. Nouvelle Sér. A, 87, Univ. Claude-Bernard, Lyon, 1987, pp. i-ii, 1-62.  Google Scholar

[2]

Trans. Am. Math. Soc., 319 (1990), 631-661. doi: 10.1090/S0002-9947-1990-0998124-1.  Google Scholar

[3]

Braunschweig: Vieweg. 361 S., 1991. Google Scholar

[4]

Progress in Mathematical Physics 42. Basel: Birkhäuser. xvi+441 pp., 2006.  Google Scholar

[5]

J. Nonlinear Sci., 18 (2008), 221-276. (English). doi: 10.1007/s00332-007-9012-8.  Google Scholar

[6]

Preprint, arXiv:1109.4515v1. (2011). Google Scholar

[7]

Preprint, arXiv:1009.0713. (2010). Google Scholar

[8]

Ph. D. thesis, EPFL, Lausanne, 2011. Google Scholar

[9]

arXiv:0910.1538, to appear in "Indiana University Mathematics Journal'' (2011). Google Scholar

[10]

Trans. Amer. Math. Soc., 363 (2011), 2967-3013. doi: 10.1090/S0002-9947-2011-05220-7.  Google Scholar

[11]

Geometriae Dedicata, 158 (2011), 1-12.  Google Scholar

[12]

London Mathematical Society Lecture Note Series, 124, Cambridge University Press, Cambridge, 1987. doi: 10.1017/CBO9780511661839.  Google Scholar

[13]

Adv. Math., 154 (2000), 46-75. doi: 10.1006/aima.1999.1892.  Google Scholar

[14]

London Mathematical Society Lecture Note Series, 213, Cambridge University Press, Cambridge, 2005. Google Scholar

[15]

Cambridge Studies in Advanced Mathematics. 91. Cambridge: Cambridge University Press. 2003. x+173 pp.  Google Scholar

[16]

Nonlinearity, 19 (2006), 1313-1348. (English). doi: 10.1088/0951-7715/19/6/006.  Google Scholar

[17]

Progress in Mathematics (Boston, Mass.), 222. Boston, MA: Birkhäuser. 2004, xxxiv+497 pp.  Google Scholar

[18]

C. R., Math., Acad. Sci. Paris, 346 (2008), 1279-1282. doi: 10.1016/j.crma.2008.10.003.  Google Scholar

[19]

Ph. D. thesis, Instituto de Matemática Pura e Aplicada, 2009. Google Scholar

[20]

C. R. Acad. Sci. Paris Sér. I Math., 306 (1988), 557-560.  Google Scholar

[21]

Proc. London Math. Soc. (3), 29 (1974), 699-713. doi: 10.1112/plms/s3-29.4.699.  Google Scholar

[22]

J. London Math. Soc. (2), 21 (1980), 544-556.  Google Scholar

[23]

Trans. Amer. Math. Soc., 180 (1973), 171-188. doi: 10.1090/S0002-9947-1973-0321133-2.  Google Scholar

[24]

J. Math. Soc. Japan, 40 (1988), 705-727. doi: 10.2969/jmsj/04040705.  Google Scholar

[25]

Mechanics day (Waterloo, ON, 1992), 207-231, Fields Inst. Commun., 7, Amer. Math. Soc., Providence, RI, 1996.  Google Scholar

[26]

J. Symplectic Geom., 6 (2008), 353-378.  Google Scholar

[27]

Complex and Differential Geometry, Springer Proceedings in Mathematics, Springer Berlin, 8 (2010), 403-420. Google Scholar

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