{"paper":{"title":"Bi-invariant metrics and quasi-morphisms on groups of Hamiltonian diffeomorphisms of surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.SG"],"primary_cat":"math.GT","authors_text":"Michael Brandenbursky","submitted_at":"2013-06-14T09:48:04Z","abstract_excerpt":"Let \\Sigma_g be a closed orientable surface let Diff_0(\\Sigma_g; area) be the identity component of the group of area-preserving diffeomorphisms of \\Sigma_g. In this work we present an extension of Gambaudo-Ghys construction to the case of a closed hyperbolic surface \\Sigma_g, i.e. we show that every non-trivial homogeneous quasi-morphism on the braid group on n strings of \\Sigma_g defines a non-trivial homogeneous quasi-morphism on the group Diff_0(\\Sigma_g; area). As a consequence we give another proof of the fact that the space of homogeneous quasi-morphisms on Diff_0(\\Sigma_g; area) is inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3350","kind":"arxiv","version":3},"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"}