Nielsen numbers and Lefschetz numbers on solvmanifolds

DOI10.2140/pjm.1991.147.153zbMath0666.55002OpenAlexW1978457115MaRDI QIDQ1116490

Christopher K. McCord

Publication date: 1991

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.1991.147.153

zbMATH Keywords

nilmanifoldNielsen numberLefschetz numbercontinuous self-map on a compact solvmanifoldfibering over a torushomotopic to a fiber- preserving map

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Fixed-point and coincidence theorems (topological aspects) (54H25) Degree, winding number (55M25) Fixed points and coincidences in algebraic topology (55M20) Fiber bundles in algebraic topology (55R10)

Related Items (17)

Two, more readily computable equivariant Nielsen numbers I. Nielsen theory for \(\mathbf M\)-ads ⋮ Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds. I ⋮ Addition formulae for Nielsen numbers and for Nielsen type numbers of fibre preserving maps ⋮ Addition formulae for Nielsen numbers and Nielsen type numbers of fibre preserving maps defined locally ⋮ Calculation of Nielsen periodic numbers of fibre preserving maps ⋮ Homotopy minimal periods for maps of three-dimensional solvmanifolds ⋮ Lefschetz and Nielsen coincidence numbers on nilmanifolds and solvmanifolds ⋮ Lefschetz and Nielsen coincidence numbers on nilmanifolds and solvmanifolds. II ⋮ Nielsen Numbers of Homotopically Periodic Maps on Infrasolvmanifolds ⋮ Fixed points on model solvmanifold pairs ⋮ Nielsen fixed point theory for partially ordered sets ⋮ Nielsen Numbers of Periodic Maps on Solvmanifolds ⋮ Nielsen type numbers for periodic points of fibre preserving maps ⋮ Twisted Lefschetz numbers of infra-solvmanifolds and algebraic groups ⋮ Product formula for the fixed point index of a fibre preserving map defined locally ⋮ Averaging Formula for Nielsen Numbers of Maps on Infra-Solvmanifolds of Type (R) ⋮ The absolute degree and Nielsen root number of a fibre-preserving map

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