Assembly Maps for Group Extensions in $K$-Theory and $L$-Theory with Twisted Coefficients

TL;DR

This paper proves that the Farrell-Jones isomorphism conjectures hold for group extensions in algebraic K- and L-theory with twisted coefficients, demonstrating inheritance of these conjectures in such extensions.

Contribution

It establishes that the Farrell-Jones conjectures are preserved under group extensions for assembly maps with twisted coefficients in K- and L-theory.

Findings

Farrell-Jones conjectures are inherited in group extensions

Assembly maps with twisted coefficients are preserved

Results apply to algebraic K- and L-theory

Abstract

In this paper we show that the Farrell-Jones isomorphism conjectures are inherited in group extensions for assembly maps in algebraic $K$-theory and $L$-theory with twisted coefficients.