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arXiv · 0806.4976

Geometry of configuration spaces of tensegrities

Franck Doray·Oleg Karpenkov·Jan Schepers
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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 tensegrity 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. Based on numerous examples we give a description of geometric conditions defining the strata for plane tensegrities, we conjecture that the list of such conditions is sufficient to describe any stratum. We conclude the paper with particular examples of strata for tensegrities in the plane with a small number of vertices.

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Franck Doray, Oleg Karpenkov, Jan Schepers. 2008-06-30. Geometry of configuration spaces of tensegrities. https://arxiv.org/abs/0806.4976

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