Periods of homeomorphisms on some compact spaces

© 2016 University of Houston. The objective of the present paper is to provide information on the set of periodic points of a homeomorphism defined in the following compact spaces: 𝕊n (the n-dimensional sphere), 𝕊n x 𝕊m (the product space of the n-dimensional with the m-dimensional spheres), ℂPn (the n- dimensional complex projective space) and ℍPn (the n-dimensional quaternion projective space). We use as main tool the action of the homeomorphism on the homology groups of these compact spaces.