On the Lefschetz periodic point free continuous self-maps on connected compact manifolds (Q719522)

A continuous map \(f: M \to M\) on a compact manifold \(M\) is said to be Lefshetz periodic point free if Lefschetz numbers of its iterates are all equal to zero, i.e., \(L(f^m)=0\) for every \(m=1,2,\ldots\). The authors characterize Lefschetz periodic point free maps on the \(n\)-dimensional (\(n\geq 1\)) complex projective space \(\mathbb{C}P^n\), the quaternion projective space \(\mathbb{H}P^n\), the sphere \(\mathbb{S}^n\) and the product of spheres \(\mathbb{S}^p \times \mathbb{S}^q\), where \(1\leq p \leq q\). Their characterization is provided in terms of conditions on induced maps on homology groups \(f_{*k}: H_k(M,\mathbb{Q})\to H_k(M,\mathbb{Q})\).