FI-hyperhomology and ordered configuration spaces
arXiv:1903.02722
Abstract
Using a result of Guès on FI-hyperhomology (a variant of a result of Gan-Li) and a semi-simplicial resolution of configuration spaces due to Kupers-Miller-Tran, we establish an explicit stable range for cohomological representation stability for configuration spaces of distinct ordered points in a manifold. Our bounds on generation degree were a factor of 5/2 better than those previously established at the time this paper was first posted. This updated article replaces an older version, which contained a mistake pointed out to us by Nicolas Guès. We are grateful to Guès for identifying the error and suggesting the resolution.
This version of the paper corrects an error in the previous (and published) version of the paper. We thank Nicolas Guès for alerting us to the error, and suggesting how to resolve it. 10 pages, 1 figure