Height functions on products of spheres and associated Reeb digraphs and level sets

[2608.00556] Height functions on products of spheres and associated Reeb digraphs and level sets Skip to main content Search Submit Donate Log in Mathematics > Differential Geometry arXiv:2608.00556 (math) [Submitted on 1 Aug 2026 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: Height functions on products of spheres and associated Reeb digraphs and level sets Authors: Naoki Kitazawa View PDF HTML (experimental) Abstract: Height functions are fundamental and important objects and tools in mathematics, especially in geometry such as differential topology and differential geometry and some related singularity theory of differentiable maps. Our interest, especially interest of the author, lies in obtaining explicit lists of such functions. Recently, as information on so-called higher degrees, he is also interested in their naturally defined 1st derivatives. We consider natural maps on products of spheres which are variants of specific cases of so-called moment maps on toric symplectic manifolds. We also generalize cases of the canonical projections of the unit spheres. This is a further result on related previous study of the author. We use Reeb graphs, graphs being natural quotient spaces of manifolds of the domains of nice functions such as Morse-Bott functions, and consisting of connected components of level sets. They are fundamental tools and objects since the last century. Comments: 21 pages. 2 figures. This is submitted as a replacement based on the directions, after the initial submission. The previous version of " 2608.00556 " (" 2608.00556v1 ") is still valid Subjects: Differential Geometry (math.DG) ; Algebraic Geometry (math.AG); Dynamical Systems (math.DS); Metric Geometry (math.MG) Cite as: arXiv:2608.00556 [math.DG] (or arXiv:2608.00556v2 [math.DG] for this version) https://doi.org/10.48550/arXiv.2608.00556 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Naoki Kitazawa [ view email ] [v1] Sat, 1 Aug 2026 09:21:36 UTC (54 KB) [v2] Tue, 25 Aug 2026 09:20:11 UTC (33 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.DG < prev | next > new | recent | 2026-08 Change to browse by: math math.AG math.DS math.MG 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)

Related documents

• Height functions on products of spheres and associated Reeb digraphs and level sets#670710
• A characterization of two-depth Journé packing for bi-parameter and Zygmund rectangles#925228
• A characterization of two-depth Journé packing for bi-parameter and Zygmund rectangles#920992
• Russell–Myhill and grounding#745550
• A Survey of Star Product Geometry#643460