E-Theory for C*-algebras over topological spaces

TL;DR

This paper develops E-theory for separable C*-algebras over topological spaces, establishing foundational properties, approximation techniques, invertibility criteria, and a universal multicoefficient theorem for specific spaces.

Contribution

It introduces E-theory for C*-algebras over topological spaces and proves key properties, including an approximation theorem and a universal multicoefficient theorem.

Findings

Established basic properties of E-theory over topological spaces

Derived an approximation theorem relating general and finite approximations

Proved a universal multicoefficient theorem for certain spaces

Abstract

We define E-theory for separable C*-algebras over second countable topological spaces and establish its basic properties. This includes an approximation theorem that relates the E-theory over a general space to the E-theories over finite approximations to this space. We obtain effective criteria for determining the invertibility of E-theory elements over possibly infinite-dimensional spaces. Furthermore, we prove a Universal Multicoefficient Theorem for C*-algebras over totally disconnected metrisable compact spaces.