Coarse cone quotients

2025/07/02 by Ulrich Bunke, Bunke, Ulrich
Computer Science · Mathematics · #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2507.01412

openalex publication_date 2025/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study the coarse motive of the quotient O^∞(X)//G of the cone of a uniform bornological coarse space X with G-action. If X admits a sufficiently ergodic probability measure, then we show that the coarse assembly map for O^∞(X)//G is not an equivalence. The main ideas are taken from a recent paper by C. Kitsios, T. Schick and F. Vigolo (arXiv:2504.21811) and adapted to the formalism of coarse homotopy theory based on bornological coarse spaces developed by A. Engel and the author.

Citations

• Coarse Baum-Connes and warped cones: failure of surjectivity in odd degree
• Roe algebras of coarse spaces via coarse geometric modules
• A Markovian and Roe-algebraic approach to asymptotic expansion in measure
• Asymptotic expansion in measure and strong ergodicity
• Discrete fundamental groups of Warped Cones and expanders
• Rigidity of warped cones and coarse geometry of expanders
• Coarse assembly maps
• Homotopy theory with bornological coarse spaces
• Kazhdan projections, random walks and ergodic theorems
• Higher index theory for certain expanders and Gromov monster groups I

Related

• Lifting coarse homotopies
• Finite asymptotic dimension and the coarse assembly map
• Homotopy theory with bornological coarse spaces
• Generalized bornological coarse spaces and coarse motivic spectra
• A Bott periodicity theorem for ℓ^p-spaces and the coarse Novikov conjecture at infinity