Asymptotic Lipschitz maps, combable groups and higher signatures
type: Item
instance of: scholarly article
title: Asymptotic Lipschitz maps, combable groups and higher signatures
zbMATH Open document ID: 0962.57018
author: Yanyan Li
published in: Geometric and Functional Analysis. GAFA
publication date: 2001-06-11T00:00:00Z
full work available at URL: http://cds.cern.ch/record/361700
review text: Let \(\Gamma\) be a torsion-free finitely generated group admitting a proper combing of bounded multiplicity. It is proved that in this case the analytic assembly map is rationally injective. In particular, the higher signatures of \(\Gamma\) are oriented homotopy invariants. The proof is based on a family of asymptotically proper Lipschitz maps from Rips complexes to Euclidean spaces used to construct a natural morphism \(E(\widetilde{P}_i/\Gamma,*)\to E(C^*(\Gamma),{\mathbb C})\), where \(\widetilde{P}_i/\Gamma\) are tubular neighbourhoods of a family of approximations of \(B\Gamma\) by finite complexes and \(E\) denotes \(E\)-theory of Connes and Higson.
Mathematics Subject Classification ID: 57R20
Mathematics Subject Classification ID: 58J22
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 46L80
Mathematics Subject Classification ID: 57R19
Mathematics Subject Classification ID: 19K35
Mathematics Subject Classification ID: 19K56
zbMATH DE Number: 1443216
zbMATH Keywords: asymptotic map
zbMATH Keywords: Lipschitz map
zbMATH Keywords: combable group
zbMATH Keywords: assembly map
reviewed by: Vladimir M. Manuilov
MaRDI profile type: Publication
OpenAlex ID: W2092606244
DOI: 10.1007/S000390050002
description: scientific article; zbMATH DE number 1443216