The geodesic complexity of n-dimensional Klein bottles
Algebraic Topology
2019-12-17 v1 Combinatorics
Abstract
The geodesic complexity of a metric space X is the smallest k for which there is a partition of X x X into ENRs E_0,...,E_k on each of which there is a continuous choice of minimal geodesic sigma(x_0,x_1) from x_0 to x_1. We prove that the geodesic complexity of an n-dimensional Klein bottle equals 2n. Its topological complexity remains unknown for n>2.
Cite
@article{arxiv.1912.07411,
title = {The geodesic complexity of n-dimensional Klein bottles},
author = {Donald M. Davis and David Recio-Mitter},
journal= {arXiv preprint arXiv:1912.07411},
year = {2019}
}