{"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/simplified-sft-moduli-spaces-for-legendrian","title":"Simplified SFT moduli spaces for Legendrian links","arxiv_id":"2104.00505","date":"2021-04-01","proceeding":null,"authors":["Russell Avdek"],"abstract":"We study moduli spaces $\\mathcal{M}$ of holomorphic maps $U$ from Riemann surfaces to $\\mathbb{R}^{4}$ with boundaries on the Lagrangian cylinder over a Legendrian link $\\Lambda \\subset (\\mathbb{R}^{3}, \\xi_{std})$. We allow our domains, $\\Sigma$, to have non-trivial topology in which case $\\mathcal{M}$ is the zero locus of an obstruction function $\\mathcal{O}$, sending a moduli space of holomorphic maps in $\\mathbb{C}$ to $H^{1}(\\Sigma)$. In general, $\\mathcal{O}^{-1}(0)$ is not combinatorially computable. However after a Legendrian isotopy, $\\Lambda$ can be made left-right-simple, implying that any $U$ of index $1$ is a disk with one or two positive punctures for which $\\pi_{\\mathbb{C}}\\circ U$ is an embedding. Moreover, any $U$ of index $2$ is either a disk or an annulus with $\\pi_{\\mathbb{C}} \\circ U$ simply covered and without interior critical points. Therefore any SFT invariant of $\\Lambda$ is combinatorially computable using only disks with $\\leq 2$ positive punctures.","url_abs":"https://arxiv.org/abs/2104.00505v4","url_pdf":"https://arxiv.org/pdf/2104.00505v4.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":"simplified-sft-moduli-spaces-for-legendrian","repo_url":"https://github.com/ravdek/legendrian_links","is_official":0,"mentioned_in_paper":0,"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}