Oriented robot motion planning in Riemannian manifolds
Geometric Topology
2021-05-05 v2 Algebraic Topology
Abstract
We consider the problem of robot motion planning in an oriented Riemannian manifold as a topological motion planning problem in its oriented frame bundle. For this purpose, we study the topological complexity of oriented frame bundles, derive an upper bound for this invariant and certain lower bounds from cup length computations. In particular, we show that for large classes of oriented manifolds, e.g. for spin manifolds, the topological complexity of the oriented frame bundle is bounded from below by the dimension of the base manifold.
Cite
@article{arxiv.1810.06281,
title = {Oriented robot motion planning in Riemannian manifolds},
author = {Stephan Mescher},
journal= {arXiv preprint arXiv:1810.06281},
year = {2021}
}
Comments
18 pages, revised version, to appear in Topology and its Applications