title: Axial distances in discrete Möbius groups.
abstract: We describe here new lower bounds for the trace of the commutator of a discrete two-generator group of Möbius transformations. These results lead to sharp estimates for the distance between the axes of elliptics in a discrete group and hence to new bounds for the volume of hyperbolic manifolds and orbifolds that will be discussed elsewhere.
authors.affiliation: Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA.
authors.forename: F W
authors.initials: FW
authors.lastname: Gehring
authors.forename: G J
authors.initials: GJ
authors.lastname: Martin