Document Type
Article
Publication Date
10-1-2014
Published In
Geometriae Dedicata
Abstract
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.
Recommended Citation
Don H. Shimamoto and Mary K. Wootters , '08.
(2014).
"Configuration Spaces Of Convex And Embedded Polygons In The Plane".
Geometriae Dedicata.
Volume 172,
Issue 1.
121-134.
DOI: 10.1007/s10711-013-9910-x
https://works.swarthmore.edu/fac-math-stat/82
Comments
This work is a preprint that is freely available from arXiv.org at arXiv:0811.1365, courtesy of Springer Verlag.
The final publication version can be freely accessed courtesy of Springer Nature's SharedIt service.