The Geometric Realization of a Semi-Simplicial Complex

1957/03/01 by John Milnor · 282 citations
Computer Science · Mathematics · #Abstract simplicial complex #Advanced Topics in Algebra #Algebra over a field #Homotopy and Cohomology in Algebraic Topology #Mathematics #Pure mathematics #Realization (probability) #Simplicial approximation theorem #Simplicial complex #Simplicial homology #Simplicial manifold #Simplicial set #Statistics #Topological and Geometric Data Analysis

paper · doi:10.2307/1969967

published in Annals of Mathematics 65(2), 357 (Princeton University)

openalex publication_date 1957/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

homology and homotopy groups. The terminology for semi-simplicial complexes will follow John Moore [7]. In particular the face and degeneracy maps of K will be denoted by d: Kn Kn-1 and si:K. -> Kn+1 respectively. 1. The definition

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