The Geometry of Configuration Spaces for Closed Chains in Two and Three Dimensions

  title={The Geometry of Configuration Spaces for Closed Chains in Two and Three Dimensions},
  author={R. James Milgram and Jeff Trinkle},
In this note we analyze the topology of the spaces of configurations in the euclidian space R of all linearly immersed polygonal circles with either fixed lengths for the sides or one side allowed to vary. Specifically, this means that the allowed maps of a k-gon 〈l1, l2, . . . , lk〉 where the li are the lengths of the successive sides, are specified by an ordered k-tuple of points in R, P1, P2, . . . , Pk with d(Pi, Pi+1) = li, 1 ≤ i ≤ k − 1 and d(Pk, P1) = lk. The most useful cases are when n… CONTINUE READING
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