{"paper":{"title":"Volumes of Discrete Groups and Topological Complexity of Homology Spheres","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"dg-ga","authors_text":"Alexander Reznikov","submitted_at":"1995-06-25T14:45:43Z","abstract_excerpt":"We address two fundamental and well-known problems of Gromov and Lyndon:\n \\demo{Problem A} (Gromov, see [5]). Consider a category $M_n$ of closed manifolds of dimension $n$ with nonzero-degree ways as morphisms. Study a partial order $M \\ge N \\Leftrightarrow Mor (M, N) \\neq \\phi$. For which $N$ the degrees of maps $f: M \\to N$ are bounded for all $M$?\n \\demo{Problem B} (Lyndon, [12], problem 13). Extend and relate the theories of deficiency, the rate of growth and the Euler-Poincar\\'e characteristic. In particular, what influence does the deficiency have on the structure of an infinite group?"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9506010","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"}