A distance between maps via interleavings of relative Sullivan algebras

[2604.06800] A distance between maps via interleavings of relative Sullivan algebras Skip to main content Search Submit Donate Log in Mathematics > Algebraic Topology arXiv:2604.06800 (math) [Submitted on 8 Apr 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: A distance between maps via interleavings of relative Sullivan algebras Authors: Katsuhiko Kuribayashi , Takahito Naito , Kengo Sekizuka , Shun Wakatsuki , Toshihiro Yamaguchi View PDF HTML (experimental) Abstract: In this article, we consider extended tame persistence commutative differential graded algebras (CDGAs) associated with relative Sullivan algebras. In particular, if the relative Sullivan algebra is a model for a map between spaces, then the persistence CDGA is isomorphic to the persistence object obtained by a Postnikov tower for the map with the polynomial de Rham functor in the homotopy category of extended tame persistence CDGAs. Moreover, the interleaving distance in the homotopy category (IHC) in the sense of Lanari and Scoccola enables us to introduce a pseudodistance on the homotopy set of maps via the persistence CDGA models for maps. In contrast to persistence cochain complexes, the IHC of persistence CDGAs does not coincide with the cohomology interleaving distance in general. Due to the reason, we also discuss formalities of a persistence CDGA with interleavings. Computational examples of the pseudodistances between maps are showcased. Comments: 42 pages Subjects: Algebraic Topology (math.AT) Cite as: arXiv:2604.06800 [math.AT] (or arXiv:2604.06800v2 [math.AT] for this version) https://doi.org/10.48550/arXiv.2604.06800 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Katsuhiko Kuribayashi [ view email ] [v1] Wed, 8 Apr 2026 08:14:57 UTC (56 KB) [v2] Fri, 28 Aug 2026 06:33:06 UTC (58 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.AT < prev | next > new | recent | 2026-04 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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