{"paper":{"title":"The twisted Ruelle zeta function on compact hyperbolic orbisurfaces and Reidemeister-Turaev torsion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.DS","math.GT","math.RT"],"primary_cat":"math.SP","authors_text":"Jan Frahm, L\\'eo B\\'enard, Polyxeni Spilioti","submitted_at":"2021-10-13T12:42:47Z","abstract_excerpt":"Let $X$ be a compact hyperbolic surface with finite order singularities, $X_1$ its unit tangent bundle. We consider the Ruelle zeta function $R(s;\\rho)$ associated to a representation $\\rho\\colon\\pi_1(X_1)\\to\\operatorname{GL}(V_\\rho)$. If $\\rho$ does not factor through $\\pi_1(X)$, we show that the value at $0$ of the Ruelle zeta function equals the sign-refined Reidemeister-Turaev torsion of $(X_1, \\rho)$ with respect to the Euler structure induced by the geodesic flow and to the natural homology orientation of $X_1$. It generalizes Fried's conjecture to non-unitary representations, and solves"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.06683","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.06683/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}