Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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COMPUTATION OF THE NIELSEN TYPE NUMBERS FOR MAPS ON THE KLEIN BOTTLE

  • Kim, Hyun-Jung (Department of Mathematics Sogang University) ;
  • Lee, Jong-Bum (Department of Mathematics Sogang University) ;
  • Yoo, Won-Sok (Department of Applied Mathematics Kumoh National Institute of Technology)
  • Published : 2008.09.30
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Abstract

Let f : M ${\rightarrow}$ M be a self-map on the Klein bottle M. We compute the Lefschetz number and the Nielsen number of f by using the infra-nilmanifold structure of the Klein bottle and the averaging formulas for the Lefschetz numbers and the Nielsen numbers of maps on infra-nilmanifolds. For each positive integer n, we provide an explicit algorithm for a complete computation of the Nielsen type numbers $NP_n(f)$ and $N{\Phi}_{n}(f)\;of\;f^{n}$.

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References

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