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J. Korean Math. Soc. 2008; 45(3): 883-902
Printed May 1, 2008
Copyright © The Korean Mathematical Society.
Minimal sets of periods for maps on the Klein bottle
Ju Young Kim, Sung Sook Kim, and Xuezhi Zhao
Catholic University of Daegu, Paichai University, Capital Normal University
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.
Keywords: periodic point, minimum set of periods, Nielsen number, Klein bottle
MSC numbers: Primary 55M20; Secondary 57N05
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