{"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/affine-diffeomorphism-groups-are-undistorted","title":"Affine diffeomorphism groups are undistorted","arxiv_id":"1912.06537","date":"2019-12-13","proceeding":null,"authors":["Robert Tang"],"abstract":"The affine diffeomorphism group $\\mathrm{Aff}(S,q)$ of a half-translation surface $(S,q)$ comprise the self-diffeomorphisms with constant differential away from the singularities. This group coincides with the stabiliser of the associated Teichm\\\"uller disc under the action of the mapping class group on Teichm\\\"uller space. We prove that any finitely generated subgroup of $\\mathrm{Aff}(S,q)$ is undistorted in the mapping class group. We also show that the systole map restricted to the associated electrified Nielsen core in the Teichm\\\"uller disc is a quasi-isometric embedding into the curve complex.","url_abs":"https://arxiv.org/abs/1912.06537v1","url_pdf":"https://arxiv.org/pdf/1912.06537v1.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":"affine-diffeomorphism-groups-are-undistorted","repo_url":"https://github.com/rob-tang/rob-tang.github.io","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}