Directed homology and persistence modules

Directed homology and persistence modules | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Directed homology and persistence modules Eric Goubault This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3829842/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 19 Dec, 2024 Read the published version in Journal of Applied and Computational Topology → Version 1 posted 9 You are reading this latest preprint version Abstract We give a self-contained account on a construction for a directed homology theory based on modules over algebras, linking it to both persistence homology and natural homology. We study its first properties, among which relative homology and Mayer-Vietoris long exact sequences and a Kunneth formula. Directed topology natural homology persistent homology Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 19 Dec, 2024 Read the published version in Journal of Applied and Computational Topology → Version 1 posted Editorial decision: Revision requested 13 May, 2024 Reviews received at journal 12 May, 2024 Reviews received at journal 22 Apr, 2024 Reviewers agreed at journal 31 Jan, 2024 Reviewers agreed at journal 23 Jan, 2024 Reviewers invited by journal 23 Jan, 2024 Editor assigned by journal 19 Jan, 2024 Submission checks completed at journal 03 Jan, 2024 First submitted to journal 02 Jan, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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