{"paper":{"title":"Multivariate Alexander colorings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Lorenzo Traldi","submitted_at":"2018-05-06T10:47:45Z","abstract_excerpt":"We extend the notion of link colorings with values in an Alexander quandle to link colorings with values in a module $M$ over the Laurent polynomial ring $\\Lambda_{\\mu}=\\mathbb{Z}[t_1^{\\pm1},\\dots,t_{\\mu}^{\\pm1}]$. If $D$ is a diagram of a link $L$ with $\\mu$ components, then the colorings of $D$ with values in $M$ form a $\\Lambda_{\\mu}$-module $\\mathrm{Color}_A(D,M)$. Extending a result of Inoue [Kodai Math.\\ J.\\ 33 (2010), 116-122], we show that $\\mathrm{Color}_A(D,M)$ is isomorphic to the module of $\\Lambda_{\\mu}$-linear maps from the Alexander module of $L$ to $M$. In particular, suppose $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02189","kind":"arxiv","version":4},"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"}