INTEGRATION OF 2-TERM REPRESENTATIONS UP TO HOMOTOPY VIA 2-FUNCTORS

被引：5

作者：

Brahic, Olivier ^{[1
]}

Ortiz, Cristian ^{[2
]}

机构：

[1] Univ Fed Parana, Dept Matemat, Setor Ciencias Exatas, Ctr Politecn, BR-81531990 Curitiba, Parana, Brazil

[2] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010,Cidade Univ, BR-05508090 Sao Paulo, Brazil

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 372卷 / 01期

关键词：

Differential geometry; Poisson geometry; LIE; INTEGRABILITY; GROUPOIDS;

D O I：

10.1090/tran/7586

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a representation up to homotopy of a Lie algebroid on a 2-term complex of vector bundles, we define the corresponding holonomy as a strict 2-functor from a Weinstein path 2-groupoid to the gauge 2-groupoid of the underlying 2-term complex. We construct a corresponding transformation 2-groupoid, and we prove that the 1-truncation of this 2-groupoid is isomorphic to the Weinstein groupoid of the VB-algebroid associated with a representation up to homotopy.

引用

页码：503 / 543

页数：41

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