{"paper":{"title":"A Markov theorem for generalized plat decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Alessia Cattabriga, Bo\\v{s}tjan Gabrov\\v{s}ek","submitted_at":"2018-01-15T12:14:54Z","abstract_excerpt":"We prove a Markov theorem for tame links in a connected closed orientable 3-manifold $M$ with respect to a plat-like representation. More precisely, given a genus $g$ Heegaard surface $\\Sigma_g$ for $M$ we represent each link in $M$ as the plat closure of a braid in the surface braid group $B_{g,2n}=\\pi_1(C_{2n}(\\Sigma_g))$ and analyze how to translate the equivalence of links in $M$ under ambient isotopy into an algebraic equivalence in $B_{g,2n}$. First, we study the equivalence problem in $\\Sigma_g\\times [0,1]$, and then, to obtain the equivalence in $M$, we investigate how isotopies corres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04766","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}