## Splitting with Continuous Control in Algebraic K-theory (2002)

by
David Rosenthal

Citations: | 10 - 5 self |

### BibTeX

@TECHREPORT{Rosenthal02splittingwith,

author = {David Rosenthal},

title = {Splitting with Continuous Control in Algebraic K-theory},

institution = {},

year = {2002}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. In this work, the continuously controlled assembly map in algebraic K-theory, as developed by Carlsson and Pedersen, is proved to be a split injection for groups Γ that satisfy certain geometric conditions. The group Γ is allowed to have torsion, generalizing a result of Carlsson and Pedersen. Combining this with a result of John Moody, K0(kΓ) is proved to be isomorphic to the colimit of K0(kH) over the finite subgroups H of Γ, when Γ is a virtually polycyclic group and k is a field of characteristic zero. 1.