E-Theory for C*-algebras over topological 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.

33 pages

References in corpus (5)

• Homological algebra in bivariant K-theory and other triangulated categories
• C*-Algebras over Topological Spaces: The Bootstrap Class
• C*-Algebras over Topological Spaces: Filtrated K-Theory
• Fiberwise KK-equivalence of continuous fields of C*-algebras
• Continuous Fields of Kirchberg C*-algebras

Cited by in corpus (12)

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• Absorbing representations with respect to closed operator convex cones
• Categorical approach to the Baum-Connes conjecture for étale groupoids
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• Homotopy-theoretic E-theory and n-order
• Classification of ${\mathcal{O}}_{\infty }$-stable $C^{\ast }$-algebras
• E-theory Spectra for graded C*-algebras
• A Bott periodicity proof for real graded $C^{\ast }$-algebras
• Graph $C^{\ast }$-algebras with a $T_1$ primitive ideal space
• One-parameter continuous fields of Kirchberg algebras with rational K-theory
• E-theory for C[0,1]-algebras with finitely many singular points
• Classification of certain continuous fields of Kirchberg algebras