{"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/skein-module-dimensions-of-mapping-tori-of","title":"Skein module dimensions of mapping tori of the 2-torus","arxiv_id":"2304.07332","date":"2023-04-14","proceeding":null,"authors":["Patrick Kinnear"],"abstract":"We determine the dimension of the Kauffman bracket skein module at generic $q$ for mapping tori of the 2-torus, generalising the well-known computation of Carrega and Gilmer. In the process, we give a decomposition of the twisted Hochschild homology of the $G$-skein algebra for $G = \\mathrm{SL}_N$ or $\\mathrm{GL}_N$, which is a direct summand of the whole skein module, and from which the dimensions follow easily in the cases $G = \\mathrm{SL}_2$ and $G = \\mathrm{GL}_1$.","url_abs":"https://arxiv.org/abs/2304.07332v3","url_pdf":"https://arxiv.org/pdf/2304.07332v3.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":"skein-module-dimensions-of-mapping-tori-of","repo_url":"https://github.com/patrickkinnear/skein-dimensions","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}