{"paper":{"title":"A class function on the mapping class group of an orientable surface and the Meyer cocycle","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Masatoshi Sato","submitted_at":"2007-12-25T11:32:14Z","abstract_excerpt":"In this paper we define a $\\mathbf{QP}^1$-valued class function on the mapping class group $\\mathcal{M}_{g,2}$ of a surface $\\Sigma_{g,2}$ of genus $g$ with two boundary components. Let $E$ be a $\\Sigma_{g,2}$ bundle over a pair of pants $P$. Gluing to $E$ the product of an annulus and $P$ along the boundaries of each fiber, we obtain a closed surface bundle over $P$. We have another closed surface bundle by gluing to $E$ the product of $P$ and two disks.\n  The sign of our class function cobounds the 2-cocycle on $\\mathcal{M}_{g,2}$ defined by the difference of the signature of these two surfa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.4060","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"}