• 제목/요약/키워드: Reidemeister sets

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REIDEMEISTER ORBIT SETS ON THE MAPPING TORUS

  • Lee, Seoung-Ho
    • 대한수학회논문집
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    • 제19권4호
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    • pp.745-757
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    • 2004
  • The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. Let f : G $\longrightarrow$ G be an endomorphism between the fundamental group of the mapping torus. Extending Jiang and Ferrario's works on Reidemeister sets, we obtain algebraic results such as addition formulae for Reidemeister orbit sets of f relative to Reidemeister sets on suspension groups. In particular, if f is an automorphism, an similar formula for Reidemeister orbit sets of f relative to Reidemeister sets on given groups is also proved.

IRREDUCIBLE REIDEMEISTER ORBIT SETS

  • Lee, Seoung Ho
    • 충청수학회지
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    • 제27권4호
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    • pp.721-734
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    • 2014
  • The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. Extending our work on Reidemeister orbit sets, we obtain algebraic results such as addition formulae for irreducible Reidemeister orbit sets. Similar formulae for Nielsen type irreducible essential orbit numbers are also proved for fibre preserving maps.

REIDEMEISTER SETS OF ITERATES

  • Lee, Seoung Ho
    • 충청수학회지
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    • 제16권1호
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    • pp.15-23
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    • 2003
  • In order to compute the Nielsen number N(f) of a self-map $f:X{\rightarrow}X$, some Reidemeister classes in the fundamental group ${\pi}_1(X)$ need to be distinguished. D. Ferrario has some algebraic results which allow distinguishing Reidemeister classes. In this paper we generalize these results to the Reidemeister sets of iterates.

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A RELATIVE REIDEMEISTER ORBIT NUMBER

  • Lee, Seoung-Ho;Yoon, Yeon-Soo
    • 대한수학회논문집
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    • 제21권1호
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    • pp.193-209
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    • 2006
  • The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. In this paper, extending Cardona and Wong's work on relative Reidemeister numbers, we show that the Reidemeister orbit numbers can be used to calculate the relative essential orbit numbers. We also apply the relative Reidemeister orbit number to study periodic orbits of fibre preserving maps.

MINIMAL SETS OF PERIODS FOR MAPS ON THE KLEIN BOTTLE

  • Kim, Ju-Young;Kim, Sung-Sook;Zhao, Xuezhi
    • 대한수학회지
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    • 제45권3호
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    • pp.883-902
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    • 2008
  • 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.