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The geodesic complexity of n-dimensional Klein bottles (1912.07411v1)
Published 16 Dec 2019 in math.AT and math.CO
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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