{"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/systolic-geometry-of-translation-surfaces","title":"Systolic geometry of translation surfaces","arxiv_id":"1809.10327","date":"2018-09-27","proceeding":null,"authors":["Tobias Columbus","Frank Herrlich","Bjoern Muetzel","Gabriela Weitze-Schmithüsen"],"abstract":"In this paper we investigate the systolic landscape of translation surfaces for fixed genus and fixed angles of their cone points. We furthermore study how the systoles of a translation surface relate to the systoles of its graph of saddle connections. This allows us to develop an algorithm to compute the systolic ratio of origamis in the stratum $\\mathcal{H}(1,1)$. We compute the maximal systolic ratio of all origamis in $\\mathcal{H}(1,1)$ with up to 67 squares. These computations support a conjecture of Judge and Parlier about the maximal systolic ratio in $\\mathcal{H}(1,1)$.","url_abs":"https://arxiv.org/abs/1809.10327v4","url_pdf":"https://arxiv.org/pdf/1809.10327v4.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":"systolic-geometry-of-translation-surfaces","repo_url":"https://github.com/mathobi/systoles","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}