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arXiv · 1712.02784

Dirac Surfaces and Threefolds

Geoffrey Scott
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Abstract

We describe Dirac structures on surfaces and 3-manifolds. Every Dirac structure on a surface $M$ is described either by a regular 1-foliation or by a section of a circle bundle obtained as a fiberwise compactification of the line bundle $\wedge^2TM$. Every Dirac structure on a 3-manifold $M$ is either the union of a presymplectic manifold and a foliated Poisson manifold, or the union of a Poisson manifold and a foliated presymplectic manifold.

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Geoffrey Scott. 2017-12-07. Dirac Surfaces and Threefolds. https://arxiv.org/abs/1712.02784

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