JGM
The leaf space of a multiplicative foliation
M. Jotz
Journal of Geometric Mechanics 2012, 4(3): 313-332 doi: 10.3934/jgm.2012.4.313
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.
keywords: Lie groupoids multiplicative structures Poisson groupoids. foliations

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