Relative hyperbolicity, classifying spaces, and lower algebraic K-theory

Abstract

For $\Gamma$ a relatively hyperbolic group, we construct a model for the universal space among $\Gamma$-spaces with isotropy on the family VC of virtually cyclic subgroups of $\Gamma$. We provide a recipe for identifying the maximal infinite virtually cyclic subgroups of Coxeter groups which are lattices in $O^+(n,1)= \iso(\mathbb H^n)$. We use the information we obtain to explicitly compute the lower algebraic K-theory of the Coxeter group $>$ (a non-uniform lattice in $O^{+}(3,1)$). Part of this computation involves calculating certain Waldhausen Nil-groups for $\mathbb{Z}[D_2]$, $\mathbb{Z}[D_3]$.

24 pages, some commutative diagrams

References in corpus (1)

• A Model for the Universal Space for Proper Actions of a Hyperbolic Group

Cited by in corpus (4)

• Lower algebraic K-theory of certain reflection groups
• Algebraic K-theory of hyperbolic 3-simplex reflection groups
• Relating the Farrell Nil-groups to the Waldhausen Nil-groups
• Complete Bredon cohomology and its applications to hierarchically defined groups