{"paper":{"title":"On the geometry of van Kampen diagrams of graph products of groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Anthony Genevois","submitted_at":"2019-01-14T19:49:29Z","abstract_excerpt":"In this article, we propose a geometric framework dedicated to the study of van Kampen diagrams of graph products of groups. As an application, we find information on the word and the conjugacy problems. The main new result of the paper deals with the computation of conjugacy length functions. More precisely, if $\\Gamma$ is a finite graph and $\\mathcal{G}= \\{ G_u \\mid u \\in V(\\Gamma) \\}$ a collection of finitely generated groups indexed by the vertices of $\\Gamma$, then $$\\max\\limits_{u \\in V(\\Gamma)} \\mathrm{CLF}_{G_u}(n) \\leq \\mathrm{CLF}_{\\Gamma \\mathcal{G}}(n) \\leq (D+1) \\cdot n + \\max\\lim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04538","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"}