Min-type Morse theory for configuration spaces of hard spheres

2011/08/29 by Yuliy Baryshnikov, Peter Bubenik, Matthew Kahle · 2 citations
Mathematics · Computer Science · Physics and Astronomy · #math.AT #cs.RO #math-ph #math.MP

paper · pdf · doi:10.1093/imrn/rnt012

published as Int Math Res Notices (2014) 2014 (9): 2577-2592 · Minor changes, new title

arxiv created 2011/08/29 · arxiv updated 2014/05/13

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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• Topological persistence of configuration spaces and independence complexes for digraphs

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