Computing cohomology groups that classify bundles of strongly self-absorbing C^*-algebras

2023/02/16 by Marius Dădărlat, Dadarlat, Marius, James E. McClure +3
Computer Science · Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #Topological and Geometric Data Analysis

paper · doi:10.48550/arxiv.2302.08028

openalex publication_date 2023/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Locally trivial bundles of C^*-algebras with fibre D ⊗ K for a strongly self-absorbing C^*-algebra D over a finite CW-complex X form a group E¹_D(X) that is the first group of a cohomology theory E^*_D(X). In this paper we compute these groups by expressing them in terms of ordinary cohomology and connective K-theory. To compare the C^*-algebraic version of gl₁(KU) with its classical counterpart we also develop a uniqueness result for the unit spectrum of complex periodic topological K-theory.

Related

• Computing cohomology groups that classify bundles of strongly self-absorbing C∗-algebras
• Bundles of strongly self-absorbing C^*-algebras with a Clifford grading
• Cohomology of Hopf C^*-algebras and Hopf von Neumann algebras
• Strongly self-absorbing C*-algebras
• Cyclic cohomology for graded C^*,r-algebras and its pairings with van Daele K-theory