Vertical configuration spaces and their homology

[2103.12137] Vertical configuration spaces and their homology Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Topology arXiv:2103.12137 (math) [Submitted on 22 Mar 2021 ( v1 ), last revised 29 Apr 2022 (this version, v3)] Title: Vertical configuration spaces and their homology Authors: Andrea Bianchi , Florian Kranhold View a PDF of the paper titled Vertical configuration spaces and their homology, by Andrea Bianchi and 1 other authors View PDF HTML (experimental) Abstract: We introduce ordered and unordered configuration spaces of 'clusters' of points in an Euclidean space $\mathbb{R}^d$, where points in each cluster satisfy a 'verticality' condition, depending on a decomposition $d=p+q$. We compute the homology in the ordered case and prove homological stability in the unordered case. Comments: 29 pages, 9 figures; accepted version Subjects: Algebraic Topology (math.AT) MSC classes: 55R80, 55R25, 55R20, 55M99 Report number: CPH-GEOTOP-DNRF151 Cite as: arXiv:2103.12137 [math.AT] (or arXiv:2103.12137v3 [math.AT] for this version) https://doi.org/10.48550/arXiv.2103.12137 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Quarterly Journal of Mathematics, vol. 73(4), 2022, pp. 1279-1306 Related DOI : https://doi.org/10.1093/qmath/haab061 Focus to learn more DOI(s) linking to related resources Submission history From: Florian Kranhold [ view email ] [v1] Mon, 22 Mar 2021 19:00:23 UTC (157 KB) [v2] Thu, 8 Apr 2021 14:08:46 UTC (158 KB) [v3] Fri, 29 Apr 2022 20:14:57 UTC (163 KB) Full-text links: Access Paper: View a PDF of the paper titled Vertical configuration spaces and their homology, by Andrea Bianchi and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.AT < prev | next > new | recent | 2021-03 Change to browse by: math 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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