On the asymptotic homotopy type of inductive limit \(C^*\)-algebras
type: Item
instance of: scholarly article
title: On the asymptotic homotopy type of inductive limit \(C^*\)-algebras
zbMATH Open document ID: 0791.46047
DOI: 10.1007/BF01459523
published in: Mathematische Annalen
publication date: 1994-04-26T00:00:00Z
full work available at URL: https://eudml.org/doc/165152
review text: Let \(X\), \(Y\) be compact, connected, metrisable spaces with base points \(x_ 0\), \(y_ 0\) and let \({\mathcal K}\) denote the compact operators. It is shown that \(C_ 0(X\setminus x_ 0)\otimes {\mathcal K}\) is asymptotically homotopic (or shape equivalent) to \(C_ 0(Y\setminus y_ 0)\otimes {\mathcal K}\) if and only if \(X\) and \(Y\) have isomorphic \(K\)-groups. Similar results are obtained for certain inductive limits of nuclear \(C^*\)- algebras.
Mathematics Subject Classification ID: 46L80
Mathematics Subject Classification ID: 46L85
zbMATH DE Number: 537337
zbMATH Keywords: compact, connected, metrisable spaces
zbMATH Keywords: base points
zbMATH Keywords: compact operators
zbMATH Keywords: asymptotically homotopic
zbMATH Keywords: shape equivalent
zbMATH Keywords: isomorphic \(K\)-groups
zbMATH Keywords: inductive limits of nuclear \(C^*\)-algebras
author: Marius Dadarlat
MaRDI profile type: Publication
cites work: Shape theory for $C^*$-algebras.
cites work: Non-commutative differential geometry
cites work: Q5748452
cites work: A note on asymptotic homomorphisms
cites work: Q3788535
cites work: Q5813687
cites work: Categories of fractions and excision in KK-theory
cites work: THE OPERATORK-FUNCTOR AND EXTENSIONS OFC*-ALGEBRAS
cites work: The role of 𝐾-theory in noncommutative algebraic topology
cites work: The Künneth theorem and the universal coefficient theorem for Kasparov's generalized K-functor
OpenAlex ID: W1970612509
description: scientific article; zbMATH DE number 537337