De Rham cohomology of diffeological spaces and foliations

被引：9

作者：

Hector, G. ^{[2
]}

Macias-Virgos, E. ^{[1
]}

Sanmartin-Carbon, E. ^{[3
]}

机构：

[1] Univ Santiago de Compostela, Dept Xeometria & Topoloxia, Santiago De Compostela 15782, Spain

[2] Math Univ Lyon 1, Inst C Jordan UMR CNRS 5028, F-69622 Villeurbanne, France

[3] Univ Vigo, Dept Matemat, F CC EE, Vigo 36310, Spain

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 2011年 / 21卷 / 3-4期

关键词：

Diffeological space; De Rham cohomology; Foliation; Base-like cohomology; LIE FOLIATIONS; INTEGRALS;

D O I：

10.1016/j.indag.2011.04.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (M, F) be a foliated manifold. We prove that there is a canonical isomorphism between the complex of base-like forms Omega(b)*(M, F) of the foliation and the "De Rham complex" of the space of leaves M/F when considered as a "diffeological" quotient. Consequently, the corresponding cohomology groups H-b*(M, F) and H*(M/F) are isomorphic. (C) 2011 Royal Netherlands Academy of Arts and Sciences. Published by Elsevier B.V. All rights reserved.

引用

页码：212 / 220

页数：9

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