This is joint work with Bob MacPherson. We study the configuration space config(n,w) of n non-overlapping disks of unit diameter in an infinite strip of width w. Our main result establishes the rate of growth of the Betti numbers for fixed j and w as n → ∞. We identify three regions in the (j,w) plane exhibiting qualitatively different topological behavior. We describe these regions as (1) a “gas” regime where homology is stable, (2) a “liquid” regime where homology is unstable, and (3) a “solid” regime where homology is trivial. We describe the boundaries between stable, unstable, and trivial homology for every n ≥ 3.

May 20, 2019 | 02:15 PM

Technische Universität Berlin

Institut für Mathematik

Straße des 17. Juni 136

10623 Berlin

Room MA 041 (Ground Floor)