Computational topology for configuration spaces of hard disks

Abstract

We explore the topology of configuration spaces of hard disks experimentally, and show that several changes in the topology can already be observed with a small number of particles. The results illustrate a theorem of Baryshnikov, Bubenik, and Kahle that critical points correspond to configurations of disks with balanced mechanical stresses, and suggest conjectures about the asymptotic topology as the number of disks tends to infinity.

version 3: 16 pages, 11 figures; made minor changes requested by journal --- changed some color figures to black and white, and reordered bibliography to appear in order of citation rather than alphabetical order