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 C1 map f : M → M is called transversal if for all m ∈ ℕ the graph of fm intersects transversally the diagonal of M × M at each point (x, x) such that x is a fixed point of fm. 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.