On the number of Klein bottle types

@article{Squin2013OnTN,
  title={On the number of Klein bottle types},
  author={Carlo H. S{\'e}quin},
  journal={Journal of Mathematics and the Arts},
  year={2013},
  volume={7},
  pages={51 - 63}
}
  • C. Séquin
  • Published 1 June 2013
  • Mathematics
  • Journal of Mathematics and the Arts
Different geometric realizations of topological Klein bottles are discussed and analysed in terms of 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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