Poisson manifolds and their associated stacks

被引：2

作者：

Villatoro, Joel ^{[1
]}

机构：

[1] Univ Illinois, Dept Math, 273 Altgeld Hall,1409 W Green St MC 382, Urbana, IL 61801 USA

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2018年 / 108卷 / 03期

关键词：

Poisson manifold; Dirac structure; Lie groupoid; Differentiable stack; Symplectic groupoid; Morita equivalence; BRACKETS;

D O I：

10.1007/s11005-017-1012-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We associate to any integrable Poisson manifold a stack, i.e., a category fibered in groupoids over a site. The site in question has objects Dirac manifolds and morphisms pairs consisting of a smooth map and a closed 2-form. We show that two Poisson manifolds are symplectically Morita equivalent if and only if their associated stacks are isomorphic. We also discuss the non-integrable case.

引用

页码：897 / 926

页数：30

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