Deformations of Lie Groupoids

被引：9

作者：

Crainic, Marius ^{[1
]}

Mestre, Joao Nuno ^{[1
]}

Struchiner, Ivan ^{[2
]}

机构：

[1] Univ Utrecht, Dept Math, NL-3508 TA Utrecht, Netherlands

[2] Univ Sao Paulo, Dept Math, Sao Paulo, Brazil

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2020年 / 2020卷 / 21期

基金：

欧洲研究理事会; 巴西圣保罗研究基金会;

关键词：

REPRESENTATIONS; COHOMOLOGY; LINEARIZATION; HOMOTOPY; BRACKETS;

D O I：

10.1093/imrn/rny221

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study deformations of Lie groupoids by means of the cohomology which controls them. This cohomology turns out to provide an intrinsic model for the cohomology of a Lie groupoid with values in its adjoint representation. We prove several fundamental properties of the deformation cohomology including Morita invariance, a van Est theorem, and a vanishing result in the proper case. Combined with Moser's deformation arguments for groupoids, we obtain several rigidity and normal form results.

引用

页码：7662 / 7746

页数：85

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