Configuration spaces of clusters as $E_d$-algebras

[2104.02729] Configuration spaces of clusters as $E_d$-algebras Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Topology arXiv:2104.02729 (math) [Submitted on 6 Apr 2021 ( v1 ), last revised 30 May 2024 (this version, v4)] Title: Configuration spaces of clusters as $E_d$-algebras Authors: Florian Kranhold View a PDF of the paper titled Configuration spaces of clusters as $E_d$-algebras, by Florian Kranhold View PDF Abstract: It is a classical result that configuration spaces of labelled particles in $\mathbb{R}^d$ are free $E_d$-algebras and that their $d$-fold bar construction is equivalent to the $d$-fold suspension of the labelling space. In this paper, we study a variation of these spaces, namely configuration spaces of labelled clusters of particles. These configuration spaces are again $E_d$-algebras, and we give geometric models for their iterated bar construction in two different ways: one establishes a description of these configuration spaces of clusters as cellular $E_1$-algebras, and the other one uses an additional verticality constraint. In the last section, we apply these results in order to calculate the stable homology of certain vertical configuration spaces. Comments: 22 pages, 6 figures. Final version, to appear in HHA Subjects: Algebraic Topology (math.AT) MSC classes: 55R80, 55I42, 55P35, 55P48, 55P65, 18N40, 57T30 Report number: MPIM-Bonn-2021 Cite as: arXiv:2104.02729 [math.AT] (or arXiv:2104.02729v4 [math.AT] for this version) https://doi.org/10.48550/arXiv.2104.02729 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Homology, Homotopy and Applications, vol. 26(1), 2024, pp. 319-339 Related DOI : https://doi.org/10.4310/HHA.2024.v26.n1.a19 Focus to learn more DOI(s) linking to related resources Submission history From: Florian Kranhold [ view email ] [v1] Tue, 6 Apr 2021 18:00:14 UTC (156 KB) [v2] Wed, 30 Jun 2021 12:08:13 UTC (153 KB) [v3] Fri, 30 Sep 2022 13:31:39 UTC (167 KB) [v4] Thu, 30 May 2024 10:19:57 UTC (270 KB) Full-text links: Access Paper: View a PDF of the paper titled Configuration spaces of clusters as $E_d$-algebras, by Florian Kranhold View PDF TeX Source view license Current browse context: math.AT < prev | next > new | recent | 2021-04 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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