On partially periodic point free self-maps on the wedge sums of spheres

Abstract

We say that a continuous map on a topological space is partially periodic point free up period n if it does not have periodic points of periods smaller than n + 1. A weaker notion is Lefschetz partially periodic point free up period n. In the present article, we consider continuous self-maps on wedge sums of spheres. We give necessary and/or sufficient conditions for such maps to be Lefschetz partially periodic point free up some period related to the structure of the space.

Keywords:

• Lefschetz numbers
• periodic point
• wedge sum of spheres

1991 Mathematics Subject Classification::

• 37C25
• 37E15
• 55M20

Acknowledgments

The author would like to thank the anonymous referees for their remarks which helped to improve the article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.