Inequalities for Discrete Möbius Groups in Infinite Dimension

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.

Discrete Morse Inequalities on Infinite Graphs

The goal of this paper is to extend to infinite graphs the knownMorse inequalities for discrete Morse functions proved by R. Forman in the finite case. In order to get this result we shall use a special kind of infinite subgraphs on which a discrete Morse function is monotonous, namely, decreasing rays. In addition, we shall use this result to characterize infinite graphs by the number of criti...

On the Conjugacy of Möbius Groups in Infinite Dimension

In this paper, we establish some conjugacy criteria of Möbius groups in infinite dimension by using Clifford matrices. This extends the corresponding known results in finite dimensional setting.

The Order Dimension of Bruhat Order on Infinite Coxeter Groups

We give a quadratic lower bound and a cubic upper bound on the order dimension of the Bruhat (or strong) ordering of the affine Coxeter group Ãn. We also demonstrate that the order dimension of the Bruhat order is infinite for a large class of Coxeter groups.

Some Inequalities for Nilpotent Multipliers of Powerful p-Groups