The Diffeomorphism Type of Canonical Integrations Of Poisson Tensors on Surfaces

Canadian mathematical bulletin

David Martinez-Torres¹ 

[1] PUC-Rio de Janeiro, Departamento de Matemática, Gávea - 22451-900, Rio de Janeiro, Brazil

关键词: Poisson tensor;    Lie groupoid;    cotangent bundle;   

DOI  :  10.4153/CMB-2015-011-7

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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 groupoidstructure. 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 extendsresults by the author and by Bonechi, Ciccoli, Staffolani, and Tarlini.

【 授权许可】

Unknown