Lefschetz periodic point free self-maps of compact manifolds

DOI10.1016/j.topol.2012.03.011zbMath1263.37038OpenAlexW1998789481MaRDI QIDQ428810

Grzegorz Graff, Piotr Nowak-Przygodzki, Agnieszka Kaczkowska, Justyna Signerska

Publication date: 25 June 2012

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2012.03.011

zbMATH Keywords

periodic pointsLefschetz numbercohomology ringrational exterior space

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Fixed points and coincidences in algebraic topology (55M20)

Related Items (6)

A criterion for the existence of periodic points based on the eigenvalues of maps induced in cohomology ⋮ On partially periodic point free self-maps on the wedge sums of spheres ⋮ Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers ⋮ On Lefschetz periodic point free self-maps ⋮ Partially periodic point free self-maps on product of spheres and Lie groups ⋮ Periods of Morse-Smale diffeomorphisms on \(\mathbb{S}^n, \mathbb{S}^m \times \mathbb{S}^n, \mathbb{C}\mathbf{P}^n\) and \(\mathbb{H}\mathbf{P}^n\)

Cites Work

• On the Lefschetz periodic point free continuous self-maps on connected compact manifolds
• The Lefschetz numbers of iterated maps
• Duan's fixed point theorem: proof and generalization
• Wecken's theorem for periodic points in dimension at least 3
• Periodic points of equivariant maps
• Indices of the iterates of ℝ³ -homeomorphisms at fixed points which are isolated invariant sets
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