FI-hyperhomology and ordered configuration spaces
Abstract
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.
Cite
@article{arxiv.1903.02722,
title = {FI-hyperhomology and ordered configuration spaces},
author = {Jeremy Miller and Jennifer C. H. Wilson},
journal= {arXiv preprint arXiv:1903.02722},
year = {2019}
}
Comments
8 pages, 1 figure. This paper originated as the appendix to the first version of "Higher order representation stability and ordered configuration spaces of manifolds" (arXiv:1611.01920). For reasons of length we removed the appendix from the published version. We have since updated the proof and strengthened the main result. Version 2 includes minor revisions. To appear in Proc. Am. Math. Soc