Weak Wecken's theorem for periodic points in dimension 3

Volume 180 / 2003

Jerzy Jezierski Fundamenta Mathematicae 180 (2003), 223-239 MSC: Primary 55M20. DOI: 10.4064/fm180-3-2


We prove that a self-map $f : M \to M$ of a compact PL-manifold of dimension $\ge 3 $ is homotopic to a map with no periodic points of period $n$ iff the Nielsen numbers $N(f^k)$ for $k$ dividing $n$ all vanish. This generalizes the result from \cite{JeAnn} to dimension $3$.


  • Jerzy JezierskiInstitute of Mathematics
    University of Agriculture
    Nowoursynowska 159
    02-787 Warszawa, Poland

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