{"paper":{"title":"Split quasicocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Pascal Rolli","submitted_at":"2013-05-01T06:00:18Z","abstract_excerpt":"Let E be a linear isometric representation of a group \\Gamma. In this paper we construct and study a family of quasicocycles \\Gamma -> E that arise from splittings \\Gamma = A * B. Under certain assumptions on A, B and E the bounded cohomology classes associated to these quasicocycles form an infinite-dimensional subspace of H^2_b(\\Gamma,E). This is in particular the case when \\Gamma is free and E finite-dimensional or of the type l^p(\\Gamma). For the trivial target E = R we obtain a new family of quasimorphisms for which we compute the Gromov norm in bounded cohomology. This yields a linear is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0095","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"}