Bridge Positions and Plat Presentations of Links

[2410.22556] Bridge Positions and Plat Presentations of Links Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Geometric Topology arXiv:2410.22556 (math) [Submitted on 29 Oct 2024 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: Bridge Positions and Plat Presentations of Links Authors: Seth Hovland View a PDF of the paper titled Bridge Positions and Plat Presentations of Links, by Seth Hovland View PDF HTML (experimental) Abstract: This paper investigates the relationship between links in bridge position and plat presentations. We prove that Hilden double coset classes of plat presentations correspond exactly to bridge positions of a link up to bridge isotopy. This correspondence allows us to translate algebraic questions about plat presentations into geometric questions about bridge positions. Using this perspective, we re-establish several results from both frameworks. In particular, we show that there is a unique Hilden double coset class for the $n$-bridge unknot in $S^3$, and that torus knots admit a single double coset class in plat position. Finally, we discuss how this correspondence can be used to study plat closures of braids, which is the subject of ongoing research. Comments: v2. 16 pages, 12 figures, strengthened proof of main theorem, rewrote introduction and updated conclusion. Accepted for publication in JKTR Subjects: Geometric Topology (math.GT) MSC classes: 57K10 Cite as: arXiv:2410.22556 [math.GT] (or arXiv:2410.22556v2 [math.GT] for this version) https://doi.org/10.48550/arXiv.2410.22556 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Seth Hovland [ view email ] [v1] Tue, 29 Oct 2024 21:46:29 UTC (3,061 KB) [v2] Sat, 15 Aug 2026 22:55:35 UTC (3,131 KB) Full-text links: Access Paper: View a PDF of the paper titled Bridge Positions and Plat Presentations of Links, by Seth Hovland View PDF HTML (experimental) TeX Source view license Current browse context: math.GT < prev | next > new | recent | 2024-10 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

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