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Search: MSC category 53D17 ( Poisson manifolds; Poisson groupoids and algebroids )

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Martinez-Torres, David
The Diffeomorphism Type of Canonical Integrations Of Poisson tensors on Surfaces
A surface $\Sigma$ endowed with a Poisson tensor $\pi$ is known to admit canonical integration, $\mathcal{G}(\pi)$, which is a 4-dimensional manifold with a (symplectic) Lie groupoid structure. In this short note we show that if $\pi$ is not an area form on the 2-sphere, then $\mathcal{G}(\pi)$ is diffeomorphic to the cotangent bundle $T^*\Sigma$. This extends results by the author and by Bonechi, Ciccoli, Staffolani, and Tarlini.

Keywords:Poisson tensor, Lie groupoid, cotangent bundle
Categories:58H05, 55R10, 53D17

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