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

DOI10.2140/agt.2008.8.563zbMath1159.55003OpenAlexW2145290908MaRDI QIDQ2426843

Xuezhi Zhao, Jong Bum Lee

Publication date: 14 May 2008

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/agt.2008.8.563

zbMATH Keywords

homotopy minimal period3-solvmanifoldsNielsen type periodic point numbers

Mathematics Subject Classification ID

Fixed points and coincidences in algebraic topology (55M20)

Related Items

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 ⋮ The R∞ property for crystallographic groups of Sol14 ⋮ Anosov theorem for coincidences on special solvmanifolds of type $(\mathrm {R})$ ⋮ Nielsen coincidence theory on infra-solvmanifolds of Sol ⋮ Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds ⋮ 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 ⋮ The \(R_\infty\) property for crystallographic groups of Sol ⋮ Crystallographic groups of Sol

Cites Work

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• Nielsen type numbers and homotopy minimal periods for maps on the 3-nilmanifolds
• 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.
• Homotopy minimal periods for \(NR\)-solvmanifolds maps
• Minimal sets of periods for torus maps via Nielsen numbers
• The Anosov theorem for exponential solvmanifolds
• Wecken's theorem for periodic points in dimension at least 3
• COMPUTATION OF THE NIELSEN TYPE NUMBERS FOR MAPS ON THE KLEIN BOTTLE
• Left invariant metrics and curvatures on simply connected three-dimensional Lie groups
• The Geometries of 3-Manifolds