2021/09/18 by Eduardo Rêgo, Rêgo, Eduardo Francisco
Computer Science · Mathematics · #57Q05 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2109.08972
openalex publication_date 2021/09/18 · openalex created_date 2021/09/27 · openalex updated_date 2026/07/28
This paper deals with the existence, or absence, of coalescent contractions of contractible spaces. These are the contractions such that when the tracks of any two points meet, at time t0, they remain together thereafter. If a finite simplicial complex K is collapsible, then any collapse of K encodes coalescent contractions of K. Examples of contractible spaces where no coalescent contractions exist are the Dunce Hat and Bing's house. We establish a criteria for contractible finite simplicial complexes that ensures there are no coalescent contractions: the star-disc property. Keywords: contractible spaces, coalescent homotopies, dunce hat, Bing's house.