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arXiv · 1408.4689

The diffeomorphism type of canonical integrations of Poisson tensors on surfaces

David Martínez Torres
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Abstract

A surface $\Sigma$ endowed with a Poisson tensor $\pi$ is known to admit a canonical integration $\mathcal{G}(\pi)$, which is a 4-dimensional manifold with a (symplectic) groupoid structure. In this short note we show that when $\pi$ is not an area form on the 2-sphere, then $\mathcal{G}(\pi)$ is diffeomorphic to the cotangent bundle $T^*\Sigma$, this extending results in \cite{Ma09} and \cite{BCST12}.

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David Martínez Torres. 2014-08-20. The diffeomorphism type of canonical integrations of Poisson tensors on surfaces. https://arxiv.org/abs/1408.4689

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