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In this paper 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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Yuliy Baryshnikov
Peter Bubenik
Matthew Kahle
International Mathematics Research Notices
Institute for Advanced Study
Urbana University
Cleveland State University
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Baryshnikov et al. (Fri,) studied this question.
www.synapsesocial.com/papers/6a03fcd3698efa300d893b1e — DOI: https://doi.org/10.1093/imrn/rnt012