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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?"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"dg-ga/9506010","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"dg-ga","submitted_at":"1995-06-25T14:45:43Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"b65dc29c7d34f9ccc42c2cce8286192eceba4830673b5ba14ecfc844c5568cb4","abstract_canon_sha256":"658875e65768efd36d76aee9d5c2e27f6934a7e84e4b74f3691255f8410757e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:48.635090Z","signature_b64":"0Miaacl2oCdMnZ93IF0fo9l6nl9GXWQLYEav42WPx6vmlCaPdm9CqKjKvMUDcLozDAw9ssACEKw4bxUEX1O0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4b51cc97bacafa1052412798ea22f70f620ce4bf5cd140508b8c8d5578d121b","last_reissued_at":"2026-05-18T01:06:48.634572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:48.634572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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]). 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