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
收藏
页码：212 / 220
页数：9
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