Real projective space as a space of planar polygons
Algebraic Topology
2015-01-19 v2 Geometric Topology
Abstract
We prove that real projective space RP^{n-3} is homeomorphic to the space of all isometry classes of n-gons in the plane with one side of length n-2 and all other sides of length 1. This makes the topological complexity of real projective space more relevant to robotics.
Keywords
Cite
@article{arxiv.1501.02821,
title = {Real projective space as a space of planar polygons},
author = {Donald M. Davis},
journal= {arXiv preprint arXiv:1501.02821},
year = {2015}
}
Comments
Improved geometric figures, minor clarifications. This version submitted for publication