{"paper":{"title":"Dimension invariants of outer automorphism groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GT"],"primary_cat":"math.GR","authors_text":"Dieter Degrijse, Juan Souto","submitted_at":"2016-02-13T16:53:57Z","abstract_excerpt":"The geometric dimension for proper actions $\\underline{\\mathrm{gd}}(G)$ of a group $G$ is the minimal dimension of a classifying space for proper actions $\\underline{E}G$. We construct for every integer $r\\geq 1$, an example of a virtually torsion-free Gromov-hyperbolic group $G$ such that for every group $\\Gamma$ which contains $G$ as a finite index normal subgroup, the virtual cohomological dimension $\\mathrm{vcd}(\\Gamma)$ of $\\Gamma $ equals $\\underline{\\mathrm{gd}}(\\Gamma)$ but such that the outer automorphism group $\\mathrm{Out}(G)$ is virtually torsion-free, admits a cocompact model for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04354","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"}