The geodesic complexity of n-dimensional Klein bottles
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 E0,...,Ek on each of which there is a continuous choice of minimal geodesic sigma(x0,x1) from x0 to x1. 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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