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The leaf space of a multiplicative foliation

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  • 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.
    Mathematics Subject Classification: Primary: 58H05, 53C12; Secondary: 22A22, 53D17.


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