 

Donald M. Davis and
David RecioMitter
The geodesic complexity of ndimensional Klein bottles
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print


Published: 
February 3, 2021. 
Keywords: 
geodesic, topological complexity, Klein bottle, polytope. 
Subject: 
53C22, 55M30, 68T40. 


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 E_{0},...,E_{k} on each of which there is a continuous choice of minimal geodesic σ(x_{0},x_{1}) from x_{0} to x_{1}. We prove that the geodesic complexity of an
ndimensional Klein bottle K_{n} equals 2n. The topological complexity of K_{n} remains unknown for n greater than 2. 

Acknowledgements
N/A


Author information
Donald M. Davis:
Department of Mathematics
Lehigh University
Bethlehem, PA 18015, USA
dmd1@lehigh.edu
David RecioMitter:
Department of Mathematics
Lehigh University
Bethlehem, PA 18015, USA
dar318@lehigh.edu

