Title

Configuration Spaces Of Convex And Embedded Polygons In The Plane

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.

Comments

This work is a preprint available from arXiv.org at arXiv:0811.1365.