Periodic Structure of Transversal Maps on $$\mathbb{C }$$ P $$^{n}$$ , $$\mathbb{H }$$ P $$^{n}$$ and $$\mathbb{S }^{p}\times \mathbb{S }^{q}$$

Abstract

A C 1 map f : M → M is called transversal if for all m ∈ N the graph of f m intersects transversally the diagonal of M × M at each point (x, x) being x a fixed point of f m. Let CP n be the n-dimensional complex projective space, HP n be the n-dimensional quaternion projective space and S p × S q be the product space of the p-dimensional with the q-dimensional spheres, p = q. Then for the cases M equal to CP n , HP n and S p × S q we study the set of periods of f by using the Lefschetz numbers for periodic points.

A Note on the Periodic Structure of Transversal Maps on the Torus and Products of Spheres

“…Let X be a compact manifold and f : X → X be a transversal map. Suppose ℓ(f m ) = 0, for some m. Then In [14] this theorem was used for transversal self-maps on the product of two spheres. And in [24] it was also used for transversal maps on a product of any numbers of spheres such that all the homology spaces are trivial or one-dimensional, the so-called sum-free product.…”