New family of hyperbolic knots whose Upsilon invariants are convex

[2403.13342] New family of hyperbolic knots whose Upsilon invariants are convex Skip to main content Search Submit Donate Log in Mathematics > Geometric Topology arXiv:2403.13342 (math) [Submitted on 20 Mar 2024] Title: New family of hyperbolic knots whose Upsilon invariants are convex Authors: Keisuke Himeno View PDF HTML (experimental) Abstract: The Upsilon invariant of a knot is a concordance invariant derived from knot Floer homology theory. It is a piecewise linear continuous function defined on the interval $[0,2]$. Borodzik and Hedden gave a question asking for which knots the Upsilon invariant is a convex function. It is known that the Upsilon invariant of any $L$-space knot, and a Floer thin knot after taking its mirror image, if necessary, as well, is convex. Also, we can make infinitely many knots whose Upsilon invariants are convex by the connected sum operation. In this paper, we construct infinitely many mutually non-concordant hyperbolic knots whose Upsilon invariants are convex. To calculate the full knot Floer complex, we make use of a combinatorial method for $(1,1)$-knots. Comments: 27 pages Subjects: Geometric Topology (math.GT) MSC classes: 57K10, 57K18 (Primary) 57R58 (Secondary) Cite as: arXiv:2403.13342 [math.GT] (or arXiv:2403.13342v1 [math.GT] for this version) https://doi.org/10.48550/arXiv.2403.13342 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Topology Appl. 373 (2025), Paper No. 109441, 25 pp Related DOI : https://doi.org/10.1016/j.topol.2025.109441 Focus to learn more DOI(s) linking to related resources Submission history From: Keisuke Himeno [ view email ] [v1] Wed, 20 Mar 2024 06:52:40 UTC (693 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.GT < prev | next > new | recent | 2024-03 Change to browse by: math 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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