{"paper":{"title":"Thurston norm via Fox calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kevin Schreve, Stefan Friedl, Stephan Tillmann","submitted_at":"2015-07-20T21:25:15Z","abstract_excerpt":"In 1976 Thurston associated to a $3$-manifold $N$ a marked polytope in $H_1(N;\\mathbb{R}),$ which measures the minimal complexity of surfaces representing homology classes and determines all fibered classes in $H^1(N;\\mathbb{R})$. Recently the first and the last author associated to a presentation $\\pi$ with two generators and one relator a marked polytope in $H_1(\\pi;\\mathbb{R})$ and showed that it determines the Bieri-Neumann-Strebel invariant of $\\pi$. In this paper, we show that if the fundamental group of a 3-manifold $N$ admits such a presentation $\\pi$, then the corresponding marked pol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05660","kind":"arxiv","version":1},"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"}