{"paper":{"title":"Distributional Topological Complexity of groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Alexander Dranishnikov","submitted_at":"2024-04-03T20:04:22Z","abstract_excerpt":"We study numerical invariants $d\\TC(\\Gamma)$ and $d\\cat(\\Gamma)$ of groups recently introduced in \\cite{DJ} and independently in \\cite{KW}. We compute $d\\TC$ for finite cyclic groups $\\mathbb Z_p$ with prime $p$ as well as for nonorientable surfaces of genus $g>3$ (for orientable surfaces it was computed in \\cite{DJ}). We prove the formula $$d\\TC(G\\ast H)=\\max\\{d\\TC (G),d\\TC (H), \\cd(G\\times H)\\}$$ for torsion free groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.03041","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.03041/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}