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Geometric group action : ウィキペディア英語版 | Geometric group action In mathematics, specifically geometric group theory, a geometric group action is a certain type of action of a discrete group on a metric space. ==Definition== In geometric group theory, a geometry is any proper, geodesic metric space. An action of a finitely-generated group ''G'' on a geometry ''X'' is geometric if it satisfies the following conditions: # Each element of ''G'' acts as an isometry of ''X''. # The action is cocompact, i.e. the quotient space ''X''/''G'' is a compact space. # The action is properly discontinuous, with each point having a finite stabilizer.
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「Geometric group action」の詳細全文を読む
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