The second homotopy group in terms of colorings of locally finite models\n and new results on asphericity

2014/12/15 by Jonathan Ariel Barmak, Barmak, Jonathan Ariel, Elías Gabriel Minian +1
Computer Science · Mathematics · #06A06 #55Q05 #55U10 #57M10 #57M20 #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1412.4835

openalex publication_date 2014/12/15 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

We describe the second homotopy group of any CW-complex K by analyzing the\nuniversal cover of a locally finite model of K using the notion of\nG-coloring of a partially ordered set. As applications we prove a\ngeneralization of the Hurewicz theorem, which relates the homotopy and homology\nof non-necessarily simply-connected complexes, and derive new results on\nasphericity for two-dimensional complexes and group presentations.\n

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