{"paper":{"title":"Relative second bounded cohomology of free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Cristina Pagliantini, Pascal Rolli","submitted_at":"2014-07-15T16:49:46Z","abstract_excerpt":"This paper is devoted to the computation of the space $H_b^2(\\Gamma,H;\\mathbb{R})$, where $\\Gamma$ is a free group of finite rank $n\\geq 2$ and $H$ is a subgroup of finite rank. More precisely we prove that $H$ has infinite index in $\\Gamma$ if and only if $H_b^2(\\Gamma,H;\\mathbb{R})$ is not trivial, and furthermore, if and only if there is an isometric embedding $\\oplus_\\infty^n\\mathcal{D}(\\mathbb{Z})\\hookrightarrow H_b^2(\\Gamma,H;\\mathbb{R})$, where $\\mathcal{D}(\\mathbb{Z})$ is the space of bounded alternating functions on $\\mathbb{Z}$ equipped with the defect norm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4053","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"}