Classification of generalized Seifert fiber spaces

[2409.02216] Classification of generalized Seifert fiber spaces Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Geometric Topology arXiv:2409.02216 (math) [Submitted on 3 Sep 2024 ( v1 ), last revised 9 Apr 2026 (this version, v2)] Title: Classification of generalized Seifert fiber spaces Authors: Fernando Galaz-Garcia , Jesús Núñez-Zimbrón View a PDF of the paper titled Classification of generalized Seifert fiber spaces, by Fernando Galaz-Garcia and Jes\'us N\'u\~nez-Zimbr\'on View PDF HTML (experimental) Abstract: We provide a symbolic classification of generalized Seifert fiber spaces, which were introduced by Mitsuishi and Yamaguchi in the classification of collapsing Alexandrov $3$-spaces. Additionally, we show that the canonical double branched cover of a non-manifold generalized Seifert fiber space is a Seifert manifold and compute its symbolic invariants in terms of those of the original space. Comments: We have corrected the statement and proof of Theorem B. The previous version had an incorrect value for the Euler number of the Seifert manifold appearing as double branched cover of a generalized Seifert manifold. To illustrate the main changes we have added several examples in this direction. 9 pages. To appear at the Canadian Mathematical Bulletin Subjects: Geometric Topology (math.GT) ; Differential Geometry (math.DG); Metric Geometry (math.MG) MSC classes: 53C23, 57S15 Cite as: arXiv:2409.02216 [math.GT] (or arXiv:2409.02216v2 [math.GT] for this version) https://doi.org/10.48550/arXiv.2409.02216 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jesús Núñez-Zimbrón [ view email ] [v1] Tue, 3 Sep 2024 18:40:12 UTC (16 KB) [v2] Thu, 9 Apr 2026 21:02:47 UTC (26 KB) Full-text links: Access Paper: View a PDF of the paper titled Classification of generalized Seifert fiber spaces, by Fernando Galaz-Garcia and Jes\'us N\'u\~nez-Zimbr\'on View PDF HTML (experimental) TeX Source view license Current browse context: math.GT < prev | next > new | recent | 2024-09 Change to browse by: math math.DG math.MG 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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