English

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