A split exact sequence of equivariant \(K\)-groups of virtually nilpotent groups
type: Item
instance of: scholarly article
title: A split exact sequence of equivariant \(K\)-groups of virtually nilpotent groups
zbMATH Open document ID: 0882.57020
DOI: 10.1023/A:1007772409933
author: Stratos Prassidis
published in: \(K\)-Theory
publication date: 1998-03-05T00:00:00Z
review text: Let \(\Gamma\) be a finite extension of a finitely presented torsionfree nilpotent group \(N\). Then the finite group \(G= \Gamma/N\) acts on a nil-manifold \(M_\Gamma\). There is the exact sequence of Steinberger and West involving equivariant PL-\(K\)-theory groups and their controlled analogues \[ \widetilde K^{\text{PL}}_{i,G} (M_\Gamma)_c @>f>> \widetilde K_{i, G}^{\text{PL}} (M_\Gamma) \to\widetilde K^{\text{Top}}_{i,G} (M_\Gamma) \to \widetilde K_{i-1, G}^{\text{PL}} (M_\Gamma)_c @>f>> \widetilde K_{i-1,G}^{\text{PL}} (M_\Gamma). \] In the paper the forget control maps \(f\) are studied. The main theorem says for \(G\) of odd order that \[ \widetilde K_{i,G}^{\text{PL}} (M_\Gamma)_c @>f>> \widetilde K_{i,G}^{\text{PL}} (M_\Gamma) \] is a split monomorphism for \(i\leq 1\). The result is put into context with the equivariant rigidity conjecture.
Mathematics Subject Classification ID: 57R19
Mathematics Subject Classification ID: 19B99
Mathematics Subject Classification ID: 19L47
Mathematics Subject Classification ID: 19D35
zbMATH DE Number: 1036289
zbMATH Keywords: equivariant \(K\)-theory
zbMATH Keywords: virtually nilpotent groups
zbMATH Keywords: fibering apparatus
reviewed by: Wolfgang Lück
MaRDI profile type: Publication
full work available at URL: a:1007772409933
OpenAlex ID: W2015090773
description: scientific article; zbMATH DE number 1036289