2018/08/27 by John D. Wiltshire-Gordon, Wiltshire-Gordon, John D.
Computer Science · Mathematics · #18G10 #55P10 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1808.08894
openalex publication_date 2018/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a finite graph G and a topological space Z, the graphical configuration space Conf(G, Z) is the space of functions V(G) -> Z so that adjacent vertices map to distinct points. We provide a homotopy decomposition of Conf(G, X x Y) in terms of the graphical configuration spaces in X and Y individually. By way of application, we prove a stabilization result for homology of configuration space in X x Cp as p goes to infinity. We also compute the homology of Conf(K3,T)/T, the space of ordered triples of distinct points in a torus T of rank r, where configurations are considered up to translation. In Section 2, we give an algorithm for computing homology of configuration space in a product of simplicial complexes. The method is applied to products of some sans-serif capital letters in Example 2.12.