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A note on the set of root classes

이승호
대한수학회 (The Korean Mathematical Society)|2009.07|대한수학회논문집 (Communications of the KMS)|제24권 제3호|pp. 451-458

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참고문헌

키워드

roots of map iteratesreduced orbit setsfull depth property
주제분류수학

초록

The set of root classes plays a crucial role in the Nielsen root theory. Extending Brown et al.'s work on the set of root classes of iterates of maps, we rearrange it into the reduced orbit set and show that under suitable hypotheses, any reduced orbit has the full depth property as in the Nielsen type theory of periodic orbits.

Abstract

The set of root classes plays a crucial role in the Nielsen root theory. Extending Brown et al.'s work on the set of root classes of iterates of maps, we rearrange it into the reduced orbit set and show that under suitable hypotheses, any reduced orbit has the full depth property as in the Nielsen type theory of periodic orbits.

참고문헌 (5)

  1. R. F. Brown, "Roots of iterates of maps", Topology Appl., 66, pp.129~157 (1995)
  2. B. Jiang, "Contemporary Mathematics 14 American Mathematical Society" (1983), Providence
  3. B. Jiang, "Reidemeister orbit sets", Fund. Math., 183, pp.139~156 (2004)
  4. T. Kiang, "The Theory of Fixed Point Classes" (1989), Springer
  5. E. Spanier, "Algebraic Topology" (1966), McGraw-Hill

관련 논문AI추천

A NOTE ON NIELSEN TYPE NUMBERS이승호대한수학회 · 대한수학회논문집2010 · 제25권 제2호Minimal sets of periods for maps on the Klein bottle김성숙, 김주영, Xuezhi Zhao대한수학회 · 대한수학회지2008 · 제45권 제3호A minimum theorem for the relative root Nielsen numberKi-Yeol Yang, Xuezhi Zhao대한수학회 · 대한수학회논문집2004 · 제19권 제1호Computation of the Nielsen type numbers for maps on the Klein bottle김현중, 유원석, 이종범대한수학회 · 대한수학회지2008 · 제45권 제5호A Nielsen type number of fibre preserving maps김승원, 이승호대한수학회 · 대한수학회논문집2013 · 제28권 제2호Density of the homotopy minimal periods of maps on infra-solvmanifolds of type $\R$이종범, Xuezhi Zhao대한수학회 · 대한수학회지2018 · 제55권 제2호

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