A cocompact group action is a group action on a topological space whose quotient
space is compact (Bridson and Haefliger 1999).
For an isometric action on a proper metric space,
this is equivalent to the existence of a compact subset whose translates cover the space. For example, integer translations on 
have quotient the torus 
. A geometric group
action additionally requires properness.
Cocompact Group Action
See also
Geometric Group Action, Group Action, Proper Group Action, Quotient SpaceExplore with Wolfram|Alpha
References
Bridson, M. R. and Haefliger, A. Metric Spaces of Non-Positive Curvature. Berlin, Germany: Springer-Verlag, 1999. https://doi.org/10.1007/978-3-662-12494-9.Cite this as:
Weisstein, Eric W. "Cocompact Group Action." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CocompactGroupAction.html