Homotopy minimal periods for N R-solvmanifolds maps

Jerzyt Jezierski, Jarek Kedra, Waclaw Marzantowicz

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17 Citations (Scopus)

Abstract

A natural number m is called the homotopy minimal period of a map f : X --> X if every map g homotopic to f will have periodic points of minimal period m. In this paper we give a complete description of the sets of homotopy minimal periods of a map of compact NR-solvmanifold of dimension greater than or equal to 4. In dimension 3 we are able to show this theorem for a map of completely solvable solvmanifold but the description is given as detailed listed table then. This shows that previous results for torus and compact nilmanifold extend to this case. (C) 2004 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)29-49
Number of pages21
JournalTopology and its Applications
Volume144
Issue number1-3
Early online date11 May 2004
DOIs
Publication statusPublished - 28 Oct 2004

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Keywords

  • periodic point
  • minimal period
  • minimal homotropy period
  • compact solvmanifold
  • Nielsen fixed point theory
  • Nielsen coincidence numbers
  • nilmanifolds
  • Lefschetz
  • theorem
  • points

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