{"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/a-characterization-of-tightly-triangulated-3","title":"A characterization of tightly triangulated 3-manifolds","arxiv_id":"1601.00065","date":"2016-01-01","proceeding":null,"authors":["Bhaskar Bagchi","Basudeb Datta","Jonathan Spreer"],"abstract":"For a field $\\mathbb{F}$, the notion of $\\mathbb{F}$-tightness of simplicial complexes was introduced by K\\\"uhnel. K\\\"uhnel and Lutz conjectured that any $\\mathbb{F}$-tight triangulation of a closed manifold is the most economic of all possible triangulations of the manifold. The boundary of a triangle is the only $\\mathbb{F}$-tight triangulation of a closed 1-manifold. A triangulation of a closed 2-manifold is $\\mathbb{F}$-tight if and only if it is $\\mathbb{F}$-orientable and neighbourly. In this paper we prove that a triangulation of a closed 3-manifold is $\\mathbb{F}$-tight if and only if it is $\\mathbb{F}$-orientable, neighbourly and stacked. In consequence, the K\\\"uhnel-Lutz conjecture is valid in dimension $\\leq 3$.","url_abs":"http://arxiv.org/abs/1601.00065v2","url_pdf":"http://arxiv.org/pdf/1601.00065v2.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":"a-characterization-of-tightly-triangulated-3","repo_url":"https://github.com/simpcomp-team/simpcomp","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}