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Geometriae Dedicata


This paper concerns the topology of configuration spaces of linkages whose underlying graph is a single cycle. Assume that the edge lengths are such that there are no configurations in which all the edges lie along a line. The main results are that, modulo translations and rotations, each component of the space of convex configurations is homeomorphic to a closed Euclidean ball and each component of the space of embedded configurations is homeomorphic to a Euclidean space. This represents an elaboration on the topological information that follows from the convexification theorem of Connelly, Demaine, and Rote.


This work is a preprint that is freely available from at arXiv:0811.1365, courtesy of Springer Verlag.

The final publication version can be freely accessed courtesy of Springer Nature's SharedIt service.

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