The equalities of interleaving distances and cohomology interleavings of spaces over $BS^1$

[2501.09257] The equalities of interleaving distances and cohomology interleavings of spaces over $BS^1$ Skip to main content Search Submit Donate Log in Mathematics > Algebraic Topology arXiv:2501.09257 (math) [Submitted on 16 Jan 2025 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: The equalities of interleaving distances and cohomology interleavings of spaces over $BS^1$ Authors: Katsuhiko Kuribayashi , Takahito Naito , Shun Wakatsuki , Toshihiro Yamaguchi View PDF HTML (experimental) Abstract: The cohomology interleaving distance (CohID) is defined and considered in the category of persistent differential graded modules over a field. As a consequence, we show that, in the category, the distance coincides with the homotopy commutative interleaving distance, the homotopy interleaving distance originally due to Blumberg and Lesnick, and the interleaving distance in the homotopy category in the sense of Lanari and Scoccola. Moreover, we apply the CohID to spaces over the classifying space $BS^1$ of the circle group via the singular cochain functor. Then, upper and lower bounds of the CohID are investigated with the cup-lengths of spaces over $BS^1$. As a computational example, we explicitly determine the CohID for complex projective spaces by utilizing the bottleneck distance of barcodes associated with the cohomology of the spaces. Comments: 40 pages Subjects: Algebraic Topology (math.AT) Cite as: arXiv:2501.09257 [math.AT] (or arXiv:2501.09257v2 [math.AT] for this version) https://doi.org/10.48550/arXiv.2501.09257 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Katsuhiko Kuribayashi [ view email ] [v1] Thu, 16 Jan 2025 02:56:14 UTC (43 KB) [v2] Thu, 27 Aug 2026 08:40:43 UTC (61 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.AT < prev | next > new | recent | 2025-01 Change to browse by: math References & Citations NASA ADS 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) Major funding support from

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