A remark on \(K_ 0\) of crystallographic groups
type: Item
instance of: scholarly article
title: A remark on \(K_ 0\) of crystallographic groups
zbMATH Open document ID: 0624.18004
DOI: 10.1016/0166-8641(87)90029-0
published in: Topology and its Applications
publication date: 1987-01-01T00:00:00Z
review text: Let \(\Gamma\) be a crystallographic group. F. Quinn proved a conjecture of the author and W. C. Hsiang: \(K_ 0({\mathbb{Q}} \Gamma)\simeq H_ 0({\mathbb{R}}^ n/\Gamma,\kappa_ 0)\), where \(\kappa_ 0\) denotes the coefficient sheaf on \({\mathbb{R}}^ n/\Gamma\) whose stalk over \(x\Gamma\) is \(K_ 0({\mathbb{Q}} F_ x)\), \(F_ x\) denotes the finite isotropy subgroup of \(\Gamma\) fixing \(x\in {\mathbb{R}}\) and \(x\Gamma\) denotes the orbit of x under \(\Gamma\). In this paper the author gives a counterexample to a naive extension of this conjecture to the integral group ring.
Mathematics Subject Classification ID: 18F25
Mathematics Subject Classification ID: 20H15
zbMATH DE Number: 4012856
zbMATH Keywords: algebraic K-theory
zbMATH Keywords: spectral sequence
zbMATH Keywords: discrete group
zbMATH Keywords: sheaf homology
zbMATH Keywords: crystallographic group
author: F. Thomas Farrell
reviewed by: Tong Wenting
MaRDI profile type: Publication
full work available at URL: 0166-8641(87)90029-0
OpenAlex ID: W2069178128
cites work: Grothendieck groups and Picard groups of abelian group rings
cites work: Q5562621
cites work: Lower k-theory of finite groups
cites work: The Whitehead Group of Poly-(Finite or Cyclic) Groups
cites work: Q4090512
description: scientific article; zbMATH DE number 4012856