The leaf space of a multiplicative foliation
Madeleine Jotz

TL;DR
This paper demonstrates that under certain conditions, the leaf space of a multiplicative foliation on a groupoid inherits a groupoid structure, with applications to Dirac and Poisson groupoids.
Contribution
It establishes conditions under which the leaf space of a multiplicative foliation forms a groupoid and applies this to relate Dirac and Poisson groupoids.
Findings
Leaf space inherits a groupoid structure under involutivity and completeness.
Special Dirac groupoids project to Poisson groupoids via forward Dirac maps.
Provides a new geometric framework for understanding Dirac and Poisson structures.
Abstract
We show that if a smooth multiplicative subbundle on a groupoid is involutive and satisfies completeness conditions, then its leaf space inherits a groupoid structure over the space of leaves of in . As an application, a special class of Dirac groupoids is shown to project by forward Dirac maps to Poisson groupoids.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Geometric and Algebraic Topology
