$L^p$ coarse Baum-Connes conjecture via $C_{0}$ coarse geometry

[2311.05333] $L^p$ coarse Baum-Connes conjecture via $C_{0}$ coarse geometry Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Functional Analysis arXiv:2311.05333 (math) [Submitted on 9 Nov 2023 ( v1 ), last revised 9 Jul 2025 (this version, v3)] Title: $L^p$ coarse Baum-Connes conjecture via $C_{0}$ coarse geometry Authors: Hang Wang , Yanru Wang , Jianguo Zhang , Dapeng Zhou View a PDF of the paper titled $L^p$ coarse Baum-Connes conjecture via $C_{0}$ coarse geometry, by Hang Wang and 3 other authors View PDF HTML (experimental) Abstract: In this paper, we investigate the $L^{p}$ coarse Baum-Connes conjecture for $p\in [1,\infty)$ via $C_{0}$ coarse structure, which is a refinement of the bounded coarse structure on a metric space. We prove that the $C_{0}$ version of the $L^{p}$ coarse Baum-Connes conjecture holds for a finite-dimensional simplicial complex equipped with a uniform spherical metric. Using this result, we construct an obstruction group for the $L^{p}$ coarse Baum-Connes conjecture. As an application, we show that the obstruction group vanishes under the assumption of finite asymptotic dimension, thereby providing a new proof of the $L^{p}$ coarse Baum-Connes conjecture in this case. Comments: 31 pages, to appear in Topology and its Applications Subjects: Functional Analysis (math.FA) ; K-Theory and Homology (math.KT); Operator Algebras (math.OA) MSC classes: 46L80, 55U10, 58B34 Cite as: arXiv:2311.05333 [math.FA] (or arXiv:2311.05333v3 [math.FA] for this version) https://doi.org/10.48550/arXiv.2311.05333 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Topology Appl. 373 (2025) 109518 Related DOI : https://doi.org/10.1016/j.topol.2025.109518 Focus to learn more DOI(s) linking to related resources Submission history From: Yanru Wang [ view email ] [v1] Thu, 9 Nov 2023 13:00:47 UTC (29 KB) [v2] Sun, 15 Dec 2024 11:02:01 UTC (29 KB) [v3] Wed, 9 Jul 2025 13:01:33 UTC (30 KB) Full-text links: Access Paper: View a PDF of the paper titled $L^p$ coarse Baum-Connes conjecture via $C_{0}$ coarse geometry, by Hang Wang and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.FA < prev | next > new | recent | 2023-11 Change to browse by: math math.KT math.OA References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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