{"paper":{"title":"Intersections of Loops and the Andersen-Mattes-Reshetikhin Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Patricia Cahn, Vladimir Chernov","submitted_at":"2011-05-23T21:19:51Z","abstract_excerpt":"Given two free homotopy classes $\\alpha_1, \\alpha_2$ of loops on an oriented surface, it is natural to ask how to compute the minimum number of intersection points $m(\\alpha_1, \\alpha_2)$ of loops in these two classes.\n  We show that for $\\alpha_1\\neq\\alpha_2$ the number of terms in the Andersen-Mattes-Reshetikhin Poisson bracket of $\\alpha_1$ and $\\alpha_2$ is equal to $m(\\alpha_1, \\alpha_2)$. Chas found examples showing that a similar statement does not, in general, hold for the Goldman Lie bracket of $\\alpha_1$ and $\\alpha_2$.\n  The main result of this paper in the case where $\\alpha_1, \\al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4638","kind":"arxiv","version":2},"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"}