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Reducing the number of periodic points in the smooth homotopy class of a self-map of a simply-connected manifold with periodic sequence of Lefschetz numbers

Tom 107 / 2013

Grzegorz Graff, Agnieszka Kaczkowska Annales Polonici Mathematici 107 (2013), 29-48 MSC: Primary 37C25, 55M20; Secondary 37C05. DOI: 10.4064/ap107-1-2

Streszczenie

Let $f$ be a smooth self-map of an $m$-dimensional ($m\geq 4$) closed connected and simply-connected manifold such that the sequence $\{L(f^n)\}_{n=1}^{\infty}$ of the Lefschetz numbers of its iterations is periodic. For a fixed natural $r$ we wish to minimize, in the smooth homotopy class, the number of periodic points with periods less than or equal to $r$. The resulting number is given by a topological invariant $J[f]$ which is defined in combinatorial terms and is constant for all sufficiently large $r$. We compute $J[f]$ for self-maps of some manifolds with simple structure of homology groups.

Autorzy

  • Grzegorz GraffFaculty of Applied Physics and Mathematics
    Gdańsk University of Technology
    Narutowicza 11/12
    80-233 Gdańsk, Poland
    e-mail
  • Agnieszka KaczkowskaFaculty of Applied Physics and Mathematics
    Gdańsk University of Technology
    Narutowicza 11/12
    80-233 Gdańsk, Poland
    e-mail

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