On the number of Klein bottle types


Different geometric realizations of topological Klein bottles are discussed and analyzed whether they can be smoothly transformed into one another and thus belong into the same regular homotopy class. Simple and distinct representatives for each of the four expected classes are introduced. In addition, novel and unusual geometries for Klein bottles are presented, some of them knotted, which may serve as proposals for large-scale sculptures.

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@inproceedings{Squin2013OnTN, title={On the number of Klein bottle types}, author={Carlo H. S{\'e}quin}, year={2013} }