Min-type Morse theory for configuration spaces of hard spheres

Published 15 Aug 2011 in math.AT, cs.RO, math-ph, and math.MP | (1108.3061v2)

Abstract: 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.

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