Computational topology for configuration spaces of hard disks

Details Computational topology for configuration spaces of hard disks Computational topology for configuration spaces of hard disks

2011-08-29

arxiv.org/abs/1108.5719v3

Mathematics

Algebraic Topology

version 3: 16 pages, 11 figures; made minor changes requested by journal --- changed some color figures to black and white, an

Scientific paper

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.

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