On the Lefschetz periodic point free continuous self-maps on connected compact manifolds
type: Item
instance of: scholarly article
title: On the Lefschetz periodic point free continuous self-maps on connected compact manifolds
zbMATH Open document ID: 1243.37022
author: Juan L. G. Guirao
author: Jaume Llibre
published in: Topology and its Applications
publication date: 2011-10-10T00:00:00Z
review text: 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 \(f_{*k}: H_k(M,\mathbb{Q})\to H_k(M,\mathbb{Q})\).
reviewed by: Piotr Oprocha
Mathematics Subject Classification ID: 37C25
zbMATH DE Number: 5956063
zbMATH Keywords: Lefschetz number
zbMATH Keywords: sphere
zbMATH Keywords: complex projective space
zbMATH Keywords: quaternion projective space
zbMATH Keywords: product of spheres
MaRDI profile type: Publication
full work available at URL: j.topol.2011.07.007
OpenAlex ID: W2065154180
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DOI: 10.1016/J.TOPOL.2011.07.007
description: scientific article; zbMATH DE number 5956063