{"paper":{"title":"A functorial extension of the abelian Reidemeister torsions of three-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Gwenael Massuyeau, Vincent Florens","submitted_at":"2014-03-17T10:02:17Z","abstract_excerpt":"Let $\\mathbb{F}$ be a field and let $G\\subset \\mathbb{F}\\setminus \\{0\\}$ be a multiplicative subgroup. We consider the category $\\mathcal{Cob}_G$ of $3$-dimensional cobordisms equipped with a representation of their fundamental group in $G$, and the category ${Vect}_{\\mathbb{F},\\pm G}$ of $\\mathbb{F}$-linear maps defined up to multiplication by an element of $\\pm G$. Using the elementary theory of Reidemeister torsions, we construct a \"Reidemeister functor\" from $Cob_G$ to ${Vect}_{\\mathbb{F},\\pm G}$. In particular, when the group $G$ is free abelian and $\\mathbb{F}$ is the field of fractions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4050","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"}