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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）』
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