Representation Stability for Disks in a Strip
Abstract
We consider the ordered configuration space of open unit-diameter disks in the infinite strip of width . In the spirit of Arnol'd and Cohen, we provide a finite presentation for the rational homology groups of this ordered configuration space as a twisted algebra. We use this presentation to prove that the ordered configuration space of open unit-diameter disks in the infinite strip of width exhibits a notion of first-order representation stability similar to Church--Ellenberg--Farb and Miller--Wilson's first-order representation stability for the ordered configuration space of points in a manifold. In addition, we prove that for large this disk configuration space exhibits notions of second- (and higher) order representation stability.
Keywords
Cite
@article{arxiv.2301.04678,
title = {Representation Stability for Disks in a Strip},
author = {Nicholas Wawrykow},
journal= {arXiv preprint arXiv:2301.04678},
year = {2026}
}
Comments
48 pages, 25 figures