nLab Klein bottle

Idea

A closed surface that does not admit an orientation.

The topological complexity of the Klein bottle is $4$ (with convention $TC(*)=0$ ).

Discussion of Klein bottles appearing in topological data analysis:

Robert Ghrist, Barcodes: The Persistent Topology of Data, Bull. Amer. Math. Soc. 45 (2008), 61-75 (doi:10.1090/S0273-0979-07-01191-3, pdf)

On topological complexity of the Klein bottle:

Daniel C. Cohen, Lucile Vandembroucq, Topological Complexity of the Klein bottle (2018), arXiv:1612.03133v3

Last revised on February 14, 2024 at 07:37:14. See the history of this page for a list of all contributions to it.