On Lefschetz periodic point free self-maps

Abstract

We study the periodic point free maps on connected retract of a finite simplicial complex using the Lefschetz numbers. We put special emphasis in the self-maps on the product of spheres and of the wedge sums of spheres.

Periodic structure of transversal maps on sum-free products of spheres

“…Let f : X → X be a continuous map, since the homology groups are either 1-dimensional or trivial, its induced maps on homology are f * j = (a j ) if j ∈ M , f * 0 = (1) and f * j = 0 otherwise; where the numbers a j are integers. A study of the periodic structure of a class of selfmaps on X, was done in [12]. So the Lefschetz numbers are…”

On topological entropy, Lefschetz numbers and Lefschetz zeta functions

“…In section 6, we give some remarks about the relationship between the entropy of a map and the factorization of its Lefschetz zeta function in factors of the form (1 ± t d i ) ±1 , with positive integers d i . Some results related with the ones of this paper can be found in [12,15,17,19,24].…”

A criterion for the existence of periodic points based on the eigenvalues of maps induced in cohomology

“…In this short paper we generalize the results from [5] and [2] provided for rational exterior spaces to spaces with rational cohomology isomorphic to a tensor product of a graded exterior algebra with generators in odd dimensions and a graded algebra with all elements of even degree. In doing so, we expand the methods presented in these paper to, for example manifolds arising as blow ups of CP n , all products of spheres and some bundles over spheres.…”

“…The following theorem appeared in [5] for products of even dimensional spheres. Using the same method one can prove it for a wider class of spaces.…”