Nielsen type numbers and homotopy minimal periods for maps on the 3-nilmanifolds

DOI10.1007/s11425-008-0003-5zbMath1158.55003OpenAlexW3162271842MaRDI QIDQ931528

Jong Bum Lee, Xuezhi Zhao

Publication date: 25 June 2008

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-008-0003-5

zbMATH Keywords

nilmanifoldNielsen type numberNielsen numberhomotopy minimal period

Mathematics Subject Classification ID

Fixed points and coincidences in algebraic topology (55M20) Discontinuous groups of transformations (57S30)

Related Items (11)

Nielsen type numbers and homotopy minimal periods for maps on solvmanifolds with \(\operatorname{Sol}_{1}^{4}\)-geometry ⋮ Unnamed Item ⋮ Combinatorial scheme of finding minimal number of periodic points for smooth self-maps of simply connected manifolds ⋮ Nielsen type numbers and homotopy minimal periods for maps on 3-solvmanifolds ⋮ The R∞ property for crystallographic groups of Sol14 ⋮ Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds ⋮ On the quasi-isometric and bi-Lipschitz classification of 3D Riemannian Lie groups ⋮ Estimation of the minimal number of periodic points for smooth self-maps of odd dimensional real projective spaces ⋮ Density of the homotopy minimal periods of maps on infra-solvmanifolds ⋮ Minimal number of periodic points for smooth self-maps of \(\mathbb {R}P^3\) ⋮ The Nielsen numbers of iterations of maps on infra-solvmanifolds of type (R) and periodic orbits

Cites Work

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• Unnamed Item
• Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds. I
• Minimal sets of periods for torus maps
• Homotopy minimal periods for maps of three-dimensional nilmanifolds.
• Minimal sets of periods for torus maps via Nielsen numbers
• Left invariant metrics and curvatures on simply connected three-dimensional Lie groups
• The Nielsen numbers of maps of nil-manifolds
• Anosov theorem for coincidences on nilmanifolds

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