Geometrical finiteness for hyperbolic orbifolds (Q1384314)

A discrete, torsion-free group \(\Gamma\) of isometries of a hyperbolic manifold is called geometrically finite if there exists a convex fundamental domain with finitely many sides. Author considers a generalization of this notion for hyperbolic orbifolds. For dimensions \(n > 3\), she shows there exist discrete groups that are not geometrically finite, but satisfy some finiteness volume condition and contain subgroups of arbitrarily large order.