Stable equivalence relations on 4-manifolds

[2405.06637] Stable equivalence relations on 4-manifolds Skip to main content Search Submit Donate Log in Mathematics > Geometric Topology arXiv:2405.06637 (math) [Submitted on 10 May 2024 ( v1 ), last revised 9 Oct 2025 (this version, v2)] Title: Stable equivalence relations on 4-manifolds Authors: Daniel Kasprowski , John Nicholson , Simona Veselá View PDF HTML (experimental) Abstract: Kreck's modified surgery gives an approach to classifying smooth $2n$-manifolds up to stable diffeomorphism, i.e. up to connected sum with copies of $S^n \times S^n$. In dimension 4, we use a combination of modified and classical surgery to study various stable equivalence relations which we compare to stable diffeomorphism. Most importantly, we consider homotopy equivalence up to stabilisation with copies of $S^2 \times S^2$. As an application, we show that closed oriented homotopy equivalent 4-manifolds with abelian fundamental group are stably diffeomorphic. We give analogues of the cancellation theorems of Hambleton--Kreck for stable homeomorphism for homotopy up to stabilisations. Finally, we give a complete algebraic obstruction to the existence of closed smooth 4-manifolds which are homotopy equivalent but not simple homotopy equivalent up to connected sum with $S^2 \times S^2$. Comments: 26 pages. Final version, to appear in Proceedings of the London Mathematical Society Subjects: Geometric Topology (math.GT) ; Algebraic Topology (math.AT) MSC classes: 57K40, 57N65, 57Q10, 57R67, 19J25 Report number: MPIM-Bonn-2024 Cite as: arXiv:2405.06637 [math.GT] (or arXiv:2405.06637v2 [math.GT] for this version) https://doi.org/10.48550/arXiv.2405.06637 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Proc. Lond. Math. Soc. 131 (2025), no. 5, Article ID e70101 Related DOI : https://doi.org/10.1112/plms.70101 Focus to learn more DOI(s) linking to related resources Submission history From: Daniel Kasprowski [ view email ] [v1] Fri, 10 May 2024 17:53:11 UTC (38 KB) [v2] Thu, 9 Oct 2025 14:36:54 UTC (40 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.GT < prev | next > new | recent | 2024-05 Change to browse by: math math.AT References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation 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)

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