Classification of certain continuous fields of Kirchberg algebras

TL;DR

This paper proves that K-theory cosheaves fully classify certain continuous fields of Kirchberg algebras over finite-dimensional spaces, extending classification results to new classes with finite-dimensional K-theory.

Contribution

It establishes that the K-theory cosheaf is a complete invariant for a broad class of continuous fields of Kirchberg algebras, including unital cases, with new range results.

Findings

K-theory cosheaf fully classifies these fields

Range results for fields with finite-dimensional K-theory

Extensions to unital continuous fields

Abstract

We show that the K-theory cosheaf is a complete invariant for separable continuous fields with vanishing boundary maps over a finite-dimensional compact metrizable topological space whose fibers are stable Kirchberg algebras with rational K-theory groups satisfying the universal coefficient theorem. We provide a range result for fields in this class with finite-dimensional K-theory. There are versions of both results for unital continuous fields.