Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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MINIMAL SETS OF PERIODS FOR MAPS ON THE KLEIN BOTTLE

  • Kim, Ju-Young (Department of Mathematics Catholic University of Daegu) ;
  • Kim, Sung-Sook (Department of Applied Mathematics Paichai University) ;
  • Zhao, Xuezhi (Department of Mathematics Capital Normal University)
  • Published : 2008.05.31
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Abstract

The main results concern with the self maps on the Klein bottle. We obtain the Reidemeister numbers and the Nielsen numbers for all self maps on the Klein bottle. In terms of the Nielsen numbers of their iterates, we totally determine the minimal sets of periods for all homotopy classes of self maps on the Klein bottle.

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References

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Cited by

  1. Homotopical theory of periodic points of periodic homeomorphisms on closed surfaces vol.156, pp.15, 2009, https://doi.org/10.1016/j.topol.2009.07.012
  2. Self-maps on flat manifolds with infinitely many periods vol.32, pp.6, 2012, https://doi.org/10.3934/dcds.2012.32.2223