Configuration spaces of disks in a strip, twisted algebras, persistence, and other stories

We give $\mathbb{Z}$-bases for the homology and cohomology of the configuration space $\operatorname{config}(n,w)$ of $n$ unit disks in an infinite strip of width $w$, first studied by Alpert, Kahle and MacPherson. We also study the way these spaces evolve both as $n$ increases (using the framework of representation stability) and as $w$ increases (using the framework of persistent homology). Finally, we include some results about the cup product in the cohomology and about the configuration space of unordered disks.Comment: 49 pages, 15 figures. Builds on and supersedes arXiv:2006.01240. v2 corrects problems with Sections 2 and 9 and expands and clarifies arguments elsewher