{"paper":{"title":"Secondary Characteristic Classes of Surface Bundles","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Soren Galatius","submitted_at":"2004-02-13T14:02:42Z","abstract_excerpt":"The Miller-Morita-Mumford classes associate to an oriented surface bundle $E\\to B$ a class $\\kappa_i(E) \\in H^{2i}(B;\\Z)$. In this note we define for each prime $p$ and each integer $i\\geq 1$ a secondary characteristic class $\\lambda_i(E) \\in H^{2i(p-1)-2}(B;\\Z)/\\Z\\kappa_{i(p-1)-1}$. The mod $p$ reduction $\\lambda_i(E) \\in H^*(B; \\F_p)$ has zero indeterminacy and satisfies $p\\lambda_i(E) = \\kappa_{i(p-1)-1}(E) \\in H^*(B;\\Z/p^2)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402226","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"}