{"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/an-algorithmic-method-to-compute-plat-like","title":"An algorithmic method to compute plat-like Markov moves for genus two 3-manifolds","arxiv_id":"2112.13718","date":"2021-12-27","proceeding":null,"authors":["Paolo Cavicchioli"],"abstract":"This article deals with equivalence of links in 3-manifolds of Heegaard genus 2. Starting from a description of such a manifold introduced by Casali et al., that uses 6-tuples of integers and determines a Heegaard decomposition of the manifold, we construct an algorithm (implemented in c++) which allows to find the words in $B_{2, 2n}$, the braid group on 2n strands of a surface of genus 2, that realizes the plat-equivalence for links in that manifold. In this way we extend to the case of genus 2 the result obtained by Cattabriga et al. for genus 1 manifolds. We describe explicitly the words for a notable group of manifolds.","url_abs":"https://arxiv.org/abs/2112.13718v1","url_pdf":"https://arxiv.org/pdf/2112.13718v1.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":"an-algorithmic-method-to-compute-plat-like","repo_url":"https://github.com/Paolo-Cavicchioli/6_tuple_representation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}