# American Institute of Mathematical Sciences

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
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