Geometric group action
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:
If a group G acts geometrically upon two geometries X and Y, then X and Y are quasi-isometric. Since any group acts geometrically on its own Cayley graph, any space on which G acts geometrically is quasi-isometric to the Cayley graph of G.
- Cannon, James W. (2002). "Geometric Group Theory". Handbook of geometric topology. North-Holland. pp. 261–305. ISBN 0-444-82432-4.