4-manifolds with a given boundary

[2510.18836] 4-manifolds with a given boundary Skip to main content Search Submit Donate Log in Mathematics > Geometric Topology arXiv:2510.18836 (math) [Submitted on 21 Oct 2025 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: 4-manifolds with a given boundary Authors: Anthony Conway , Daniel Kasprowski View PDF HTML (experimental) Abstract: This paper studies the homotopy and homeomorphism classifications of $4$-manifolds with boundary. Given $4$-manifolds $X_0$ and $X_1$ with fundamental group $\pi$, we consider the problem of extending a homotopy equivalence $h \colon \partial X_0 \to \partial X_1$ to a homotopy equivalence $X_0 \to X_1$. We solve this problem in broad settings for a class of groups that includes free groups, finite cyclic groups, finite dihedral groups, solvable Baumslag-Solitar groups, and many $3$-manifold groups. When the fundamental group is additionally assumed to be good, we use surgery theory to list situations when a homeomorphism $h\colon\partial X_0 \to\partial X_1$ extends to a homeomorphism $X_0 \to X_1$. The outcome recovers results of Boyer in the simply-connected case and work of the first author and Powell when $\pi \cong \mathbb{Z}$ and the $\partial X_i$ have torsion Alexander module. Comments: 68 pages. v2: Proposition 7.13 has been improved upon Subjects: Geometric Topology (math.GT) Cite as: arXiv:2510.18836 [math.GT] (or arXiv:2510.18836v2 [math.GT] for this version) https://doi.org/10.48550/arXiv.2510.18836 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Anthony Conway [ view email ] [v1] Tue, 21 Oct 2025 17:31:58 UTC (77 KB) [v2] Thu, 27 Aug 2026 23:05:25 UTC (95 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.GT < prev | next > new | recent | 2025-10 Change to browse by: math References & Citations NASA ADS 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) Major funding support from

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