Rodrı́guez, Periods for transversal maps on compact manifolds with a given homology

Communicated by the Editors ABSTRACT. Let 1M be a compact C ’ differentiable manifold such that its rational homology is H3 (M; Q) zz Q if j E J U {0}, and Hj (M; Q) z (0) otherwise. Here J is a subset of the set of natural numbers N with cardinal 1, 2 or 3. A C1 map f: A4 + A4 is called transversal if for all m E N the graph of f m intersects transversally the diagonal of A4 x M at each point (2, z) such that z is a fixed point of f”. We study the set of periods of f by using the Lefschetz numbers for periodic points. 1