The leaf space of a multiplicative foliation

M. Jotz

doi:10.3934/jgm.2012.4.313

Article Contents

2012, Volume 4, Issue 3: 313-332. Doi: 10.3934/jgm.2012.4.313

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The leaf space of a multiplicative foliation

M. Jotz^1,

1.
Section de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne

Received: November 2010

Revised: October 2011

Published: September 2012

Abstract / Introduction Related Papers Cited by

Abstract

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.

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

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