Publication

The Leaf Space Of A Multiplicative Foliation

Madeleine Jotz
2012
Journal Articles

Abstract

We show that if a smooth multiplicative subbundle S subset of T G 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 boolean AND S in P. As an application, a special class of Dirac groupoids is shown to project by forward Dirac maps to Poisson groupoids.

Official source

https://infoscience.epfl.ch/entities/publication/a89ceb2d-3aea-499a-a200-d225eed8a18b

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Madeleine Jotz
2012
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/a89ceb2d-3aea-499a-a200-d225eed8a18b

About this result

Related concepts (27)

Poisson manifold

In differential geometry, a field in mathematics, a Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises that of symplectic manifold, which in turn generalises the phase space from Hamiltonian mechanics. A Poisson structure (or Poisson bracket) on a smooth manifold is a functionon the vector space of smooth functions on , making it into a Lie algebra subject to a Leibniz rule (also known as a Poisson algebra).

Groupoid

In mathematics, especially in and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group in several equivalent ways. A groupoid can be seen as a: Group with a partial function replacing the binary operation; in which every morphism is invertible. A category of this sort can be viewed as augmented with a unary operation on the morphisms, called inverse by analogy with group theory. A groupoid where there is only one object is a usual group.

Project

A project is any undertaking, carried out individually or collaboratively and possibly involving research or design, that is carefully planned to achieve a particular goal. An alternative view sees a project managerially as a sequence of events: a "set of interrelated tasks to be executed over a fixed period and within certain cost and other limitations". A project may be a temporary (rather than a permanent) social system (work system), possibly staffed by teams (within or across organizations) to accomplish particular tasks under time constraints.

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