THE MOD H NIELSEN NUMBER

  • Received : 2009.03.24
  • Accepted : 2009.05.18
  • Published : 2009.06.30

Abstract

Let f : $X{\rightarrow}X$ be a self-map of a connected finite polyhedron X. In this short note, we say that the mod H Nielsen number $N_H(f)$ is well-defined without the algebraic condition $ f_{\pi}(H)\;{\subseteq}H$ and that $N_H(f)$ is the same as the q-Nielsen number $N_q(f)$ in any case.

Keywords

References

  1. R. Brown, The Lefschetz Fixed Point Theorem, Scott-Foresman, Grenview, IL, 1971.
  2. R. Brown, More about Nielsen theories and their applications, In: Handbook of Topological Fixed Point Theory, Kluwer, 2005, 433-462.
  3. B. Jiang, Lectures on Nielsen fixed point theory, Contemp. Math., vol.14, Amer. Math. Soc., Providence, RI, 1983.
  4. M. Woo and J. Kim, Note on a lower bound of Nielsen number, J. of Korean Math. Soc. 29 (1992), 117-125.
  5. C. You, Fixed point classes of a fiber map, Pacific J. Math. 100 (1982), 217-241. https://doi.org/10.2140/pjm.1982.100.217