A Note on the Set of Periods of Transversal Homological Sphere Self-maps

Let M be a n -dimensional manifold with the same homology than the n -dimensional sphere. A C 1 map f : M M M is called transversal if for all m ] N the graph of f m intersects transversally the diagonal of M 2 M at each point ( x , x ) such that x is a fixed point of f m . We study the minimal set of periods of f by using the Lefschetz numbers for periodic points. In the particular case that n is even, we also study the set of periods for the transversal holomorphic self-maps of M .