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

We give Z-bases for the homology and cohomology of the configuration space 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.55R80; 16S15, 18A25, 55N31, 57Q70 1. Introduction 2. Combinatorial and algebraic setup 3. Homology of weighted no-.kC1/-equal spaces 4. Decomposing cell.n;w/ into layers 5. Betti number growth function 6. Cohomology ring 7. Persistent homology 8. Relations in the twisted algebra and FI d -modules 9. Configuration spaces of unordered disks 10.Open questions and further directions Appendix.Computer calculations for small