Partially periodic point free self-maps on product of spheres and Lie groups
Let \(X\) be a topological manifold and \(f:X\to X\) a continuous map. The map \(f\) is said to be partially periodic point free up to period \(n\) if \(f\) does not have periodic points of periods smaller than \(n+1\). Similarly \(f\) is Lefschetz periodic point free if the Lefschetz numbers of all iterates of \(f\) are zero. In this paper the author considers continuous self-maps on products of any number spheres of different dimensions and present necessary and sufficient conditions for such maps to be Lefschetz periodic point free and Lefschetz partially periodic point free. The results are applied to continuous self-maps on Lie groups.
scientific article; zbMATH DE number 7259351