|
In topology, Borel−Moore homology or homology with closed support is a homology theory for locally compact spaces, introduced by . For reasonable compact spaces, Borel−Moore homology coincides with the usual singular homology. For non-compact spaces, each theory has its own advantages. In particular, a closed submanifold defines a class in Borel–Moore homology, but not in ordinary homology unless the submanifold is compact. Note: The equivariant cohomology theory for spaces with an action of a group ''G'' is sometimes called Borel cohomology; it is defined as ''H'' *''G''(''X'') = ''H'' *((''EG'' × ''X'')/''G''). That is not related to the subject of this article. ==Definition== There are several ways to define Borel−Moore homology. They all coincide for reasonable spaces such as manifolds and CW complexes. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Borel–Moore homology」の詳細全文を読む スポンサード リンク
|