{"paper":{"title":"Relative hyperbolicity, classifying spaces, and lower algebraic K-theory","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.KT","authors_text":"I. J. Ortiz, J.-F. Lafont","submitted_at":"2006-06-19T19:16:13Z","abstract_excerpt":"For $\\Gamma$ a relatively hyperbolic group, we construct a model for the universal space among $\\Gamma$-spaces with isotropy on the family VC of virtually cyclic subgroups of $\\Gamma$. We provide a recipe for identifying the maximal infinite virtually cyclic subgroups of Coxeter groups which are lattices in $O^+(n,1)= \\iso(\\mathbb H^n)$. We use the information we obtain to explicitly compute the lower algebraic K-theory of the Coxeter group $\\gt$ (a non-uniform lattice in $O^+(3,1)$). Part of this computation involves calculating certain Waldhausen Nil-groups for $\\mathbb Z[D_2]$, $\\mathbb Z[D"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606473","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"}