Topological Complexity of the Klein bottle

Abstract

We show that the (normalized) topological complexity of the Klein bottle is $4$. We also show that, for any $g\ge 2$, $TC(N_g)=4$. This completes the recent work by Dranishnikov on the topological complexity of non-orientable surfaces.

Improvements in the exposition. References added. To appear in Journal of Applied and Computational Topology

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