Periods of continuous maps on some compact spaces

Abstract

Abstract. The objective of this paper is to provide information on the set of periodic points of a continuous self-map defined in the following compact spaces: S n (the n-dimensional sphere), S n × S m (the product space of the n-dimensional with the m-dimensional spheres), CP n (the n-dimensional complex projective space) and HP n (the n-dimensional quaternion projective space). We use as main tool the action of the map on the homology groups of these compact spaces.

Periods of Morse–Smale diffeomorphisms on $${\mathbb {S}}^n$$, $${\mathbb {S}}^m \times {\mathbb {S}}^n$$, $${\mathbb {C}}{\mathbf{P }}^n$$ and $${\mathbb {H}}{\mathbf{P }}^n$$

“…Related with these results the reader can look at the set of periods for homeomorphisms (respectively, continuous maps) on S n and on S m × S n which have been studied in [13] (respectively, [14]).…”