{"paper":{"title":"The Amalgamated Product Structure of the Tame Automorphism Group in Dimension Three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"David Wright","submitted_at":"2013-10-30T21:15:20Z","abstract_excerpt":"It is shown the the tame subgroup $\\text{TA}_3(\\mathbb C)$ of the group $\\text{GA}_3(\\mathbb C)$ of polynomials automorphisms of ${\\mathbb C}^3$ can be realized as the product of three subgroups, amalgamated along pairwise intersections, in a manner that generalizes the well-known amalgamated free product structure of $\\text{TA}_2(\\mathbb C)$ (which coincides with $\\text{GA}_2(\\mathbb C)$ by Jung's Theorem). The result follows from defining relations for $\\text{TA}_3(\\mathbb C)$ given by U. U. Umirbaev."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8325","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"}