On the K-theory of groups with finite asymptotic dimension

2006/05/03 by Bartels, Arthur, Rosenthal, David
#19B28 (Primary) #19D50 (Secondary) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.math/0605088

Abstract

It is proved that the assembly maps in algebraic K- and L-theory with respect to the family of finite subgroups is injective for groups with finite asymptotic dimension that admit a finite model for the classifying space for proper actions. The result also applies to certain groups that admit only a finite dimensional model for this space. In particular, it applies to discrete subgroups of virtually connected Lie groups.

Related

• Algebraic K-theory of Geometric Groups
• Topological K-homology for non-proper actions and assembly maps
• Assembly Maps
• Equivariant stable homotopy methods in the algebraic K-theory of infinite groups
• The Behavior of Nil-Groups under Localization and the Relative Assembly Map