2020/06/01 by Hannah Alpert, Alpert, Hannah
Mathematics · #20C30 (Secondary) #55R80 (Primary) 05E10 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2006.01240
openalex publication_date 2020/06/01 · openalex created_date 2020/06/12 · openalex updated_date 2026/07/28
For fixed j and w, we study the j-th homology of the configuration space of n labeled disks of width 1 in an infinite strip of width w. As n grows, the homology groups grow exponentially in rank, suggesting a generalized representation stability as defined by Church--Ellenberg--Farb and Ramos. We prove this generalized representation stability for the strip of width 2, leaving open the case of w > 2. We also prove it for the configuration space of n labeled points in the line, of which no k are equal.