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

摘要

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) = Isom(H-n). We use the information we obtain to explicitly compute the lower algebraic K-theory of the Coxeter group Gamma(3) (a non-uniform lattice in O+(3, 1)). Part of this computation involves calculating certain Waldhausen Nil-groups for Z[D-2], Z[D-3]. (c) 2007 Elsevier Ltd. All rights reserved.