The leaf space of a multiplicative foliation

Abstract

We show that if a smooth multiplicative subbundle $S\subseteq TG$ on a groupoid $G\rr P$ 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.

References in corpus (4)

• Discrete Nonholonomic Lagrangian Systems on Lie Groupoids
• Multiplicative Dirac structures on Lie groups
• Foliated groupoids and their infinitesimal data
• Infinitesimal objects associated to Dirac groupoids and their homogeneous spaces

Cited by in corpus (2)

• Foliated groupoids and their infinitesimal data
• Infinitesimal objects associated to Dirac groupoids and their homogeneous spaces