Controlled K-theory

Controlled K - Theory

The controlled finiteness obstruction and torsion are defined using controlled algebra, giving a more algebraic proof of the topological invariance of torsion and the homotopy finiteness of compact ANRs.

Controlled K-theory I: Basic theory

This paper provides a full controlled version of algebraic K-theory. This includes a rich array of assembly maps; the controlled assembly isomorphism theorem identifying the controlled group with homology; and the stability theorem describing the behavior of the inverse limit as the control parameter goes to 0. There is a careful treatment of spectral cosheaf homology and related tools, includi...

Dynamic Asymptotic Dimension and Controlled Operator K - Theory

In earlier work the authors introduced dynamic asymptotic dimension, a notion of dimension for topological dynamical systems that applies to many interesting examples. In this paper, we use finiteness of dynamic asymptotic dimension to get information on the K-theory of the associated crossed product C ̊algebras: specifically, we give a new proof of the Baum-Connes conjecture for such actions. T...

Controlled Algebraic K-Theory of Integral Group Ring of ...

We calculate the lower Controlled Algebraic K-theory of any nitely generated innnite subgroup of SL(3; Z), the group of 3 3 integral matrices of determinant 1.ally (innnite) cyclic groups.

K - Theory