2023/01/11 by Nicholas Wawrykow, Wawrykow, Nicholas
Computer Science · Mathematics · #55U15 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2301.04678
openalex publication_date 2023/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the ordered configuration space of n open unit-diameter disks in the infinite strip of width w. In the spirit of Arnol'd and Cohen, we provide a finite presentation for the rational homology groups of this ordered configuration space as a twisted algebra. We use this presentation to prove that the ordered configuration space of open unit-diameter disks in the infinite strip of width w exhibits a notion of first-order representation stability similar to Church--Ellenberg--Farb and Miller--Wilson's first-order representation stability for the ordered configuration space of points in a manifold. In addition, we prove that for large w this disk configuration space exhibits notions of second- (and higher) order representation stability.