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(G,X)-manifold : ウィキペディア英語版 | (G,X)-manifold
In mathematics, the concept of a -manifold generalizes several different kinds of manifolds, including Riemannian manifolds, affine manifolds, piecewise linear manifolds, etc. ==Definition== Let be a group acting on a manifold via diffeomorphisms—i.e. for each , the map from to itself is a diffeomorphism. A manifold which satisfies the following conditions is called a -manifold: # There exists an open cover of and a family of diffeomorphisms taking each to an open subset of . # For each with nonempty intersection, there exists a such that for all . In other words, viewing the elements of as diffeomorphisms, each transition map is the restriction of an element of to .
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「(G,X)-manifold」の詳細全文を読む
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