Stable relations. II. Corona semiprojectivity and dimension-drop C^∗-algebras

Terry Atherton Loring

Vol. 172 (1996), No. 2, 461–475

DOI: 10.2140/pjm.1996.172.461

Abstract

We prove that the relations in any presentation of the dimension-drop interval are stable, meaning there is a perturbation of all approximate representations into exact representations. The dimension-drop interval is the algebra of all M_n-valued continuous function on the interval that are zero at one end-point and scalar at the other. This has applications to mod − p K-theory, lifting problems and classification problems in C^∗-algebras. For many applications, the perturbation must respect precise functorial conditions. To make this possible, we develop a matricial version of Kasparov’s technical theorem.

Mathematical Subject Classification 2000

Primary: 46L05

Secondary: 46L80

Milestones

Received: 3 September 1993

Revised: 15 April 1995

Published: 1 February 1996