{"paper":{"title":"A functorial extension of the Magnus representation to the category of three-dimensional cobordisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Gwenael Massuyeau, Juan Serrano de Rodrigo, Vincent Florens","submitted_at":"2016-04-23T13:42:23Z","abstract_excerpt":"Let $R$ be an integral domain and $G$ be a subgroup of its group of units. We consider the category $\\mathbf{\\mathsf{Cob}}_G$ of 3-dimensional cobordisms between oriented surfaces with connected boundary, equipped with a representation of their fundamental group in $G$. Under some mild conditions on $R$, we construct a monoidal functor from $\\mathbf{\\mathsf{Cob}}_G$ to the category $\\mathbf{\\mathsf{pLagr}}_R$ consisting of \"pointed Lagrangian relations\" between skew-Hermitian $R$-modules. We call it the \"Magnus functor\" since it contains the Magnus representation of mapping class groups as a s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06905","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"}