2013/10/11 by Spiros Adams-Florou, Adams-Florou, Spiros
Computer Science · Mathematics · Physics and Astronomy · #57Qxx #57R67 #Algebraic Topology (math.AT) #Black Holes and Theoretical Physics #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1310.3066
openalex publication_date 2013/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove that a simplicial map of finite-dimensional locally finite simplicial complexes has contractible point inverses if and only if it is an ε-controlled homotopy equivalence for all ε>0 if and only if f× id_ℝ is a bounded homotopy equivalence measured in the open cone over the target. This confirms for such a space X the slogan that arbitrarily fine control over X corresponds to bounded control over the open cone O(X+). For the proof a one parameter family of cellulations \Xε^′\_0