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arXiv · 1912.07411

The geodesic complexity of n-dimensional Klein bottles

Donald M. Davis·David Recio-Mitter
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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.

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Donald M. Davis, David Recio-Mitter. 2019-12-16. The geodesic complexity of n-dimensional Klein bottles. https://arxiv.org/abs/1912.07411

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