Periods for transversal maps via Lefschetz numbers for periodic points

Let f : M --> M be a C-1 map on a C-1 differentiable manifold. The map f is called transversal if for all m is an element of N the graph of f(m) intersects transversally the diagonal of M x M at each point (x, x) such that x is a fixed point of f(m). We study the set of periods of f by using the Lefschetz numbers for periodic points. We focus our study on transversal maps defined on compact manifolds such that their rational homology is H-0 approximate to Q, H-1 approximate to Q + Q and H-k approximate to {0} for k not equal 0, 1.