2019/03/07 by Jeremy Miller, J. Wilson, Miller, Jeremy +1
Mathematics · #18A25 #18G40 #55R40 #55R80 #55U10 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1903.02722
openalex publication_date 2019/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using a result of Gan and Li on FI-hyperhomology and a semi-simplicial resolution of configuration spaces due to Randal-Williams, we establish an improved representation stability stable range for configuration spaces of distinct ordered points in a manifold. Our bounds on generation degree improve the best known stability slope by a factor of 5/2 in the most general case. We adapt this result of Gan and Li to apply beyond stability arguments involving highly-connected simplicial complexes, and our methods suggest that their result may be widely applicable to improving most stability ranges for FI-modules in the current representation stability literature.