Continuous Control and the Algebraic L-theory Assembly Map

Abstract

In this work, the assembly map in L-theory for the family of finite subgroups is proven to be a split injection for a class of groups. Groups in this class, including virtually polycyclic groups, have universal spaces that satisfy certain geometric conditions. The proof follows the method developed by Carlsson-Pedersen to split the assembly map in the case of torsion free groups. Here, the continuously controlled techniques and results are extended to handle groups with torsion.

15 pages

References in corpus (2)

• A Model for the Universal Space for Proper Actions of a Hyperbolic Group
• Splitting With Continuous Control in Algebraic K-theory

Cited by in corpus (5)

• Orbit categories, classifying spaces, and generalized homotopy fixed points
• Split Injectivity of the Baum-Connes Assembly Map
• Equivariant Morse theory on Vietoris-Rips complexes & universal spaces for proper actions
• Coarse $\mathcal{Z}$-Boundaries for Groups
• Assembly Maps for Group Extensions in $K$-Theory and $L$-Theory with Twisted Coefficients