{"paper":{"title":"Cohomology of symplectic groups and Meyer's signature theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AT","authors_text":"Andrew Ranicki, Carmen Rovi, Caterina Campagnolo, Dave Benson","submitted_at":"2017-10-13T09:27:49Z","abstract_excerpt":"Meyer showed that the signature of a closed oriented surface bundle over a surface is a multiple of $4$, and can be computed using an element of $H^2(\\mathsf{Sp}(2g, \\mathbb{Z}),\\mathbb{Z})$. Denoting by $1 \\to \\mathbb{Z} \\to \\widetilde{\\mathsf{Sp}(2g,\\mathbb{Z})} \\to \\mathsf{Sp}(2g,\\mathbb{Z}) \\to 1$ the pullback of the universal cover of $\\mathsf{ Sp}(2g,\\mathbb{R})$, Deligne proved that every finite index subgroup of $\\widetilde{\\mathsf {Sp}(2g, \\mathbb{Z})}$ contains $2\\mathbb{Z}$. As a consequence, a class in the second cohomology of any finite quotient of $\\mathsf{Sp}(2g, \\mathbb{Z})$ ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04851","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"}