{"paper":{"title":"A note on Dehn colorings and invariant factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Derek A. Smith, Lorenzo Traldi, William Watkins","submitted_at":"2018-04-08T14:46:02Z","abstract_excerpt":"If $A$ is an abelian group and $\\phi$ is an integer, let $A(\\phi)$ be the subgroup of $A$ consisting of elements $a \\in A$ such that $\\phi \\cdot a=0$. We prove that if $D$ is a diagram of a classical link $L$ and $0=\\phi_0,\\phi_1,\\dots,\\phi_{n-1}$ are the invariant factors of an adjusted Goeritz matrix of $D$, then the group $\\mathcal{D}_{A}(D)$ of Dehn colorings of $D$ with values in $A$ is isomorphic to the direct product of $A$ and $A=A(\\phi_{0}),A(\\phi_1),\\dots,A(\\phi_{n-1})$. It follows that the Dehn coloring groups of $L$ are isomorphic to those of a connected sum of torus links $T_{(2,\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02700","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"}