{"paper":{"title":"Finding generators and relations for groups acting on the hyperbolic ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Donald I. Cartwright, Tim Steger","submitted_at":"2017-01-10T07:20:58Z","abstract_excerpt":"In order to enumerate the fake projective planes, as announced in~\\cite{CS}, we found explicit generators and a presentation for each maximal arithmetic subgroup $\\bar\\Gamma$ of~$PU(2,1)$ for which the (appropriately normalized) covolume equals~$1/N$ for some integer~$N\\ge1$. Prasad and Yeung \\cite{PY1,PY2} had given a list of all such $\\bar\\Gamma$ (up to equivalence).\n  The generators were found by a computer search which uses the natural action of $PU(2,1)$ on the unit ball $B(\\C^2)$ in~$\\C^2$. Our main results here give criteria which ensure that the computer search has found sufficiently m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02452","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"}