[1901.08027] Skeins on Branes Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Symplectic Geometry arXiv:1901.08027 (math) [Submitted on 23 Jan 2019 ( v1 ), last revised 24 Apr 2026 (this version, v6)] Title: Skeins on Branes Authors: Tobias Ekholm , Vivek Shende View a PDF of the paper titled Skeins on Branes, by Tobias Ekholm and Vivek Shende View PDF HTML (experimental) Abstract: We study 1-parameter families of holomorphic curves with Lagrangian boundary in Calabi-Yau 3-folds. We show that the expected codimension one phenomena can be organized to match the HOMFLYPT skein relations from quantum topology. It follows that counting holomorphic curves by the class of their boundaries in the skein module of the Lagrangian gives a deformation invariant result. This is a mathematically rigorous incarnation of Witten's assertion that boundaries of open topological strings create line defects in Chern-Simons theory. Using this theory, we rigorously establish the following prediction of Ooguri and Vafa: the coefficients of the HOMFLYPT polynomial of a link in the three-sphere count the holomorphic curves in the resolved conifold, with boundary on (a push-off of) the link conormal. Comments: 34 pages. Details for gluing results were added in a new Section 4 and the paper was revised Subjects: Symplectic Geometry (math.SG) ; High Energy Physics - Theory (hep-th); Geometric Topology (math.GT) Cite as: arXiv:1901.08027 [math.SG] (or arXiv:1901.08027v6 [math.SG] for this version) https://doi.org/10.48550/arXiv.1901.08027 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Tobias Ekholm [ view email ] [v1] Wed, 23 Jan 2019 18:02:25 UTC (105 KB) [v2] Sun, 6 Oct 2019 19:58:55 UTC (131 KB) [v3] Thu, 11 Feb 2021 11:41:11 UTC (131 KB) [v4] Fri, 15 Nov 2024 17:55:02 UTC (146 KB) [v5] Tue, 18 Feb 2025 13:20:17 UTC (146 KB) [v6] Fri, 24 Apr 2026 08:42:24 UTC (166 KB) Full-text links: Access Paper: View a PDF of the paper titled Skeins on Branes, by Tobias Ekholm and Vivek Shende View PDF HTML (experimental) TeX Source view license Current browse context: math.SG < prev | next > new | recent | 2019-01 Change to browse by: hep-th math math.GT References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar 2 blog links ( what is this? ) export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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