Geodesic complexity for non-geodesic spaces
Metric Geometry
2021-05-31 v4 Algebraic Topology
Abstract
We define the notion of near geodesic between points of a metric space when no geodesic exists, and use this to extend Recio-Mitter's notion of geodesic complexity to non-geodesic spaces. This has potential application to topological robotics. We determine explicit near geodesics and geodesic complexity in a variety of cases.
Cite
@article{arxiv.2009.11628,
title = {Geodesic complexity for non-geodesic spaces},
author = {Donald M. Davis},
journal= {arXiv preprint arXiv:2009.11628},
year = {2021}
}
Comments
One major correction