Min-type Morse theory for configuration spaces of hard spheres
  We study configuration spaces of hard spheres in a bounded region. We develop a general Morse-theoretic framework, and show that mechanically balanced configurations play the role of critical points. As an application, we find the precise threshold radius for a configuration space to be homotopy equivalent to the configuration space of points. 
Yuliy Baryshnikov, Peter Bubenik, Matthew Kahle
math.AT cs.RO math-ph math.MP