A stable splitting of factorisation homology of generalised surfaces

[2310.07688] A stable splitting of factorisation homology of generalised surfaces Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Topology arXiv:2310.07688 (math) [Submitted on 11 Oct 2023 ( v1 ), last revised 7 Jan 2025 (this version, v2)] Title: A stable splitting of factorisation homology of generalised surfaces Authors: Florian Kranhold View a PDF of the paper titled A stable splitting of factorisation homology of generalised surfaces, by Florian Kranhold View PDF HTML (experimental) Abstract: For a manifold $W$ and an $E_d$-algebra $A$, the factorisation homology $\int_W A$ can be seen as a generalisation of the classical configuration space of labelled particles in $W$. It carries an action by the diffeomorphism group $\mathrm{Diff}_\partial(W)$, and for the generalised surfaces $W_{g,1}:=(\#^g S^n\times S^n)\setminus\mathring D{}^{2n}$, we have stabilisation maps among the quotients $\int_{W_{g,1}} A\,/\!/\,\mathrm{Diff}_\partial(W_{g,1})$ which increase the genus $g$. In the case where a highly-connected tangential structure $\theta$ is taken into account, we describe its stable homology in terms of the iterated bar construction $\mathrm{B}^{2n}A$ and a tangential Thom spectrum $\mathrm{MT}\theta$. We also consider the question of homological stability. Comments: 39 pages; accepted version Subjects: Algebraic Topology (math.AT) MSC classes: 55R80, 57S05, 57R15, 55P47, 55P48, 18N70 Cite as: arXiv:2310.07688 [math.AT] (or arXiv:2310.07688v2 [math.AT] for this version) https://doi.org/10.48550/arXiv.2310.07688 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1112/jlms.70089 Focus to learn more DOI(s) linking to related resources Submission history From: Florian Kranhold [ view email ] [v1] Wed, 11 Oct 2023 17:36:49 UTC (273 KB) [v2] Tue, 7 Jan 2025 15:13:49 UTC (282 KB) Full-text links: Access Paper: View a PDF of the paper titled A stable splitting of factorisation homology of generalised surfaces, by Florian Kranhold View PDF HTML (experimental) TeX Source view license Current browse context: math.AT < prev | next > new | recent | 2023-10 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

Related documents

• A stable splitting of factorisation homology of generalised surfaces#611234
• Algebraic correspondences between surfaces#490324
• On symplectic and non-symplectic automorphisms of K3 surfaces#231541
• K3 surfaces with non-symplectic automorphisms of prime order#231542
• Higher Riemann-Hilbert Correspondence and Descent for Regular Foliations#927119