The soft torus and applications to almost commuting matrices
type: Item
instance of: scholarly article
title: The soft torus and applications to almost commuting matrices
zbMATH Open document ID: 0781.46048
author: Ruy Exel
published in: Pacific Journal of Mathematics
publication date: 1993-11-17T00:00:00Z
review text: The ``soft torus'' \(A_ \varepsilon\) is defined to be the universal \(C^*\)-algebra generated by a pair of unitaries for which the commutator has norm less than or equal to \(\varepsilon\). We show that the \(K\)-theory of \(A_ \varepsilon\) is naturally isomorphic to the \(K\)-theory of the algebra of continuous functions on the two-torus, although these algebras are not homotopically equivalent. This result is applied to give a new proof of the equality of certain invariants associated to almost commuting unitary matrices, namely the \(K\)-theory invariant and the winding number invariant.
Mathematics Subject Classification ID: 46L80
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 19K56
zbMATH DE Number: 446332
zbMATH Keywords: soft torus
zbMATH Keywords: universal \(C^*\)-algebra
zbMATH Keywords: \(K\)-theory
zbMATH Keywords: equality of certain invariants associated to almost commuting unitary matrices
zbMATH Keywords: \(K\)-theory invariant
zbMATH Keywords: winding number invariant
MaRDI profile type: Publication
OpenAlex ID: W1988187144
DOI: 10.2140/PJM.1993.160.207
description: scientific article; zbMATH DE number 446332