{"paper":{"title":"Torsion and fibrations","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"dg-ga","authors_text":"Thomas Schick, Thomas Thielmann, Wolfgang Lueck","submitted_at":"1997-07-10T12:38:09Z","abstract_excerpt":"We study the behaviour of analytic torsion under smooth fibrations. Namely, let F \\to E \\to^{f} B be a smooth fiber bundle of connected closed oriented smooth manifolds and let $V$ be a flat vector bundle over $E$. Assume that $E$ and $B$ come with Riemannian metrics and $V$ comes with a unimodular (not necessarily flat) Riemannian metric. Let $\\rho_{an}(E;V)$ be the analytic torsion of $E$ with coefficients in $V$ and let $\\Pf_B$ be the Pfaffian $\\dim(B)$-form. Let $H^q_{dR}(F;V)$ be the flat vector bundle over $B$ whose fiber over $b \\in B$ is $H^q_{dR}(F_b;V)$ with the Riemannian metric whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9707010","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"}