{"paper":{"title":"Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"Viacheslav V. Nikulin","submitted_at":"2006-09-09T12:26:50Z","abstract_excerpt":"After results by the author (1980, 1981), and by Vinberg (1981), finiteness of the number of maximal arithmetic reflection groups in Lobachevsky spaces was not known in dimensions $2\\le n\\le 9$ only.\n  Recently (2005), the finiteness was proved in dimension 2 by Long, Maclachlan and Reid, and in dimension 3 by Agol.\n  Here we use these results in dimensions 2 and 3 to prove finiteness in all remaining dimensions $4\\le n\\le 9$. Methods of the author (1980, 1981) are strong enough to complete this in few lines by simple considerations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609256","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"}