2014/02/13 by Justin R Smith, Smith, Justin R.
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 18G55 #Secondary 55U40 #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1402.3134
openalex publication_date 2014/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we extend earlier work by showing that if X and Y are simplicial complexes (i.e. simplicial sets whose simplices are determined by their vertices), a morphism g:N(X)→ N(Y) of Steenrod coalgebras (normalized chain-complexes equipped with extra structure) induces one of their topological realizations g:|X|→ |Y|. If g is an isomorphism, then it induces an isomorphism between X and Y, implying that they are homeomorphic.