Some new biautomatic Coxeter groups

Equivariant K-homology for Some Coxeter Groups

We obtain the equivariant K-homology of the classifying space EW for W a right-angled or, more generally, an even Coxeter group. The key result is a formula for the relative Bredon homology of EW in terms of Coxeter cells. Our calculations amount to the K-theory of the reduced C∗-algebra of W , via the Baum-Connes assembly map.

Rational Subgroups of Biautomatic Groups

Central Quotients of Biautomatic Groups

The quotient of a biautomatic group by a subgroup of the center is shown to be biautomatic. The main tool used is the Neumann-Shapiro triangulation of S, associated to a biautomatic structure on Zn. As an application, direct factors of biautomatic groups are shown to be biautomatic. Biautomatic groups form a wide class of finitely presented groups with interesting geometric and computational pr...

Essays on Coxeter groups Coxeter elements in finite Coxeter groups

A finite Coxeter group possesses a distinguished conjugacy class of Coxeter elements. The literature about these is very large, but it seems to me that there is still room for a better motivated account than what exists. The standard references on thismaterial are [Bourbaki:1968] and [Humphreys:1990], butmy treatment follows [Steinberg:1959] and [Steinberg:1985], from which the clever parts of ...

Minimal Length Elements in Some Double Cosets of Coxeter Groups

We study the minimal length elements in some double cosets of Coxeter groups and use them to study Lusztig’s G-stable pieces and the generalization of G-stable pieces introduced by Lu and Yakimov. We also use them to study the minimal length elements in a conjugacy class of a finite Coxeter group and prove a conjecture in [GKP].