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Donald M. Davis and
David Recio-Mitter
The geodesic complexity of n-dimensional Klein bottles
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| Published: |
February 3, 2021. |
| Keywords: |
geodesic, topological complexity, Klein bottle, polytope. |
| Subject: |
53C22, 55M30, 68T40. |
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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 into locally compact sets E0,...,Ek on each of which there is a continuous choice of minimal geodesic σ(x0,x1) from x0 to x1. We prove that the geodesic complexity of an
n-dimensional Klein bottle Kn equals 2n. The topological complexity of Kn remains unknown for n greater than 2. |
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| Acknowledgements
N/A
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| Author information
Donald M. Davis:
Department of Mathematics
Lehigh University
Bethlehem, PA 18015, USA
dmd1@lehigh.edu
David Recio-Mitter:
Department of Mathematics
Lehigh University
Bethlehem, PA 18015, USA
dar318@lehigh.edu
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