{"paper":{"title":"Plat closures of spherical braids in $\\mathbb{R}P^3$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Rama Mishra, Visakh Narayanan","submitted_at":"2023-04-18T12:46:18Z","abstract_excerpt":"We define plat closure for spherical braids to obtain links in $\\mathbb{R}P^3$ and prove that all links in $\\mathbb{R}P^3$ can be realized in this manner. Given a spherical braid $\\beta$ of $2n$ strands in $\\mathbb{R}P^3$ we associate a permutation $h_{\\beta}$ on $n$ elements called \\textit{residual permutation}. We prove that the number of components of the plat closure link of a spherical braid $\\beta$ is same as the number of disjoint cycles in $h_{\\beta}$. We also present a set of moves on spherical braids in the same spirit as the classical Markov moves on braids. The completeness of this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.08954","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.08954/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}