Axial distances in discrete Mobius groups.

Axial distances in discrete Möbius groups.

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.

The Mobius function of the small Ree groups

The Möbius function for a group G was introduced in 1936 by Hall in order to count ordered generating sets of G. In this paper we determine the Möbius function of the simple small Ree groups, R(q) = G2(q) where q = 3 for m > 0, using their 2-transitive permutation representation of degree q + 1. We also describe their maximal subgroups in terms of this representation. We use this to enumerate s...

Discrete Stein Characterizations and Discrete Information Distances

We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distributions and discrete information functionals. AMS 2000 subject classifications: Primary 60K35; secondary 94A17.

Structural Properties of Inner Amenable Discrete Groups

The Mobius Band and the Mobius Foliation

Some years ago we introduced a new topological invariant for foliated manifolds using techniques from noncommutative geometry, in particular the pairing between K-Theory and cyclic cohomology. The motivation came from flat principal G-bundles where the base space is a non simply connected manifold. The computation of this invariant is quite complicated. In this article we try to perform certain...