{"paper":{"title":"Hierarchically cocompact classifying spaces for mapping class groups of surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GR","authors_text":"Brita Nucinkis, Nansen Petrosyan","submitted_at":"2017-12-01T21:17:57Z","abstract_excerpt":"We define the notion of a hierarchically cocompact classifying space for a family of subgroups of a group. Our main application is to show that the mapping class group $\\mbox{Mod}(S)$ of any connected oriented compact surface $S$, possibly with punctures and boundary components and with negative Euler characteristic has a hierarchically cocompact model for the family of virtually cyclic subgroups of dimension at most $\\mbox{vcd} \\mbox{Mod}(S)+1$. When the surface is closed, we prove that this bound is optimal. In particular, this answers a question of L\\\"{u}ck for mapping class groups of surfa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00496","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"}