REVIEW 1 cited by
FI-hyperhomology and ordered configuration spaces
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original 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.
Forward citations
Cited by 1 Pith paper
-
An inductive method for $\mathrm{OI}$-modules
An explicit double-exponential upper bound on the regularity of OI-modules presented in finite degrees, together with a new inductive method for proving their structural properties.
Discussion (0). Continue with ORCID to comment.