Transgressing the algebraic coarse character map

2025/07/14 by Alexander Engel, Engel, Alexander, Matthias Ludewig +1
Computer Science · #FOS: Mathematics #K-Theory and Homology (math.KT) #Mathematics, Computing, and Information Processing #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2507.10816

openalex publication_date 2025/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We pursue an old conjecture of John Roe about the algebraic K-theory of the algebra of finite propagation, locally trace-class operators, namely that transgressing the algebraic coarse character map on this algebra to a Higson dominated corona coincides with the usual Chern character on the corona.

Citations

• Large-scale quantization of trace I: Finite propagation operators
• Coronas and Callias type operators in coarse geometry
• Coronas for properly combable spaces
• Chern Classes in Alexander-Spanier Cohomology

Related

• Transgressions and Chern characters in coarse homotopy theory
• A version of smooth K-theory adapted to the total Chern class
• Controlled K-theory and K-Homology
• Algebraic K-theory and trace invariants
• Notes on the Chern-character