{"paper":{"title":"Homotopy types of reduced 2-nilpotent simplicial groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Hans-Joachim Baues, Roman Mikhailov","submitted_at":"2008-04-12T07:43:26Z","abstract_excerpt":"We classify the homotopy types of reduced 2-nilpotent simplicial groups in terms of the homology an d boundary invariants $b,\\beta$. This contains as special cases results of J.H.C. Whitehead on 1-connected 4-dimensional complexes and of Quillen on reduced 2-nilpotent rational simplicial groups. Moreover it yields for 1-nilpotent (or abelian) simplicial groups a classification due to Dold-Kan. Our result describes a new natural structure of the integral homology of any simply connected space. We also classify the homotopy types of connective spectra in the category of 2-nilpotent simplicial gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.2000","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"}