\mathfrakS-coalgebras determine fundamental groups

2013/07/26 by Justin R Smith, Smith, Justin R.
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 18G55 #Secondary 55U40

paper · pdf · doi:10.48550/arxiv.1307.7098

openalex publication_date 2013/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we extend earlier work by showing that if X and Y are simplicial complexes (i.e. simplicial sets whose nondegenerate simplices are determined by their vertices), an isomorphism C(X)\congC(Y) of coalgebras over the Barratt-Eccles operad implies that the 3-skeleton of X is weakly equivalent to the 3-skeleton of Y, also implying that π₁(X)=π₁(Y).

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