Minimal number of periodic points for smooth self-maps of $S^3$

Volume 204 / 2009

Grzegorz Graff, Jerzy Jezierski Fundamenta Mathematicae 204 (2009), 127-144 MSC: Primary 37C25, 55M20; Secondary 37C05. DOI: 10.4064/fm204-2-3


Let $f$ be a continuous self-map of a smooth compact connected and simply-connected manifold of dimension $m\geq 3$ and $r$ a fixed natural number. A topological invariant $D^m_r[f]$, introduced by the authors [Forum Math. 21 (2009)], is equal to the minimal number of $r$-periodic points for all smooth maps homotopic to $f$. In this paper we calculate $D^3_r[f]$ for all self-maps of $S^3$.


  • Grzegorz GraffFaculty of Applied
    Physics and Mathematics
    Gdańsk University of Technology
    Narutowicza 11/12
    80-233 Gdańsk, Poland
  • Jerzy JezierskiFaculty of Applied
    Informatics and Mathematics
    Warsaw University of Life Sciences (SGGW)
    Nowoursynowska 159
    00-757 Warszawa, Poland

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