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

2024/02/14 by Marius Dădărlat, James E. McClure, Ulrich Pennig · 1 voice
Mathematics · #Advanced Operator Algebra Research #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra

paper · doi:10.1142/s1793525324500110

openalex publication_date 2024/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02

Abstract

Locally trivial bundles of [Formula: see text]-algebras with fiber [Formula: see text] for a strongly self-absorbing [Formula: see text]-algebra [Formula: see text] over a finite CW-complex [Formula: see text] form a group [Formula: see text] that is the first group of a cohomology theory [Formula: see text]. In this paper, we compute these groups by expressing them in terms of ordinary cohomology and connective [Formula: see text]-theory. To compare the [Formula: see text]-algebraic version of [Formula: see text] with its classical counterpart we also develop a uniqueness result for the unit spectrum of complex periodic topological [Formula: see text]-theory.

Discussions

• The authors explore bundles of C*-algebras over finite spaces and show how their properties can be understood using ordinary cohomology and K-theory. They also clarify the structure of topological K-t [bsky, 0 points, 0 comments]

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