Geometry of Configuration Spaces of Tensegrities |
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Authors: | Franck Doray Oleg Karpenkov Jan Schepers |
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Institution: | 1. Mathematisch Instituut, Universiteit Leiden, P.O. Box 9512, 2300 RA, Leiden, The Netherlands
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Abstract: | Consider a graph G with n vertices. In this paper we study geometric conditions for an n-tuple of points in ℝ
d
to admit a nonzero self-stress with underlying graph G. We introduce and investigate a natural stratification, depending on G, of the configuration space of all n-tuples in ℝ
d
. In particular we find surgeries on graphs that give relations between different strata. Further we discuss questions related
to geometric conditions defining the strata for plane tensegrities. We conclude the paper with particular examples of strata
for tensegrities in the plane with a small number of vertices. |
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Keywords: | |
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