{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-filtered-generalization-of-the-chekanov","title":"A filtered generalization of the Chekanov-Eliashberg algebra","arxiv_id":"2205.13031","date":"2022-05-25","proceeding":null,"authors":["Russell Avdek"],"abstract":"We define a new algebra associated to a Legendrian submanifold $\\Lambda$ of a contact manifold of the form $\\mathbb{R}_{t} \\times W$, called the planar diagram algebra and denoted $PDA(\\Lambda, \\mathcal{P})$. It is a non-commutative, filtered, differential graded algebra whose filtered stable tame isomorphism class is an invariant of $\\Lambda$ together with a partition $\\mathcal{P}$ of its connected components. When $\\Lambda$ is connected, $PDA$ is the Chekanov-Eliashberg algebra. In general, the $PDA$ differential counts holomorphic disks with multiple positive punctures using a combinatorial framework inspired by string topology.","url_abs":"https://arxiv.org/abs/2205.13031v5","url_pdf":"https://arxiv.org/pdf/2205.13031v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-filtered-generalization-of-the-chekanov","repo_url":"https://github.com/ravdek/legendrian_links","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}