Fixed points of Lie group actions on surfaces

DOI10.1017/S0143385700003345zbMath0609.57020WikidataQ115336328 ScholiaQ115336328MaRDI QIDQ3749774

Joseph F. Plante

Publication date: 1986

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

fixed point propertyexponential growthcompact surfaceminimal set3- dimensional, simply-connected Lie groupconnected finite-dimensional Lie groupnilpotent Lie group actions

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Compact Lie groups of differentiable transformations (57S15) Nilpotent and solvable Lie groups (22E25) Fixed points and coincidences in algebraic topology (55M20)

Related Items (15)

Fixed points of discrete nilpotent group actions on \(S^2\) ⋮ Common zeroes of families of smooth vector fields on surfaces ⋮ Finite orbits for nilpotent actions on the torus ⋮ Fixed points of local actions of Lie groups on real and complex 2-manifolds ⋮ Intersection of stable and unstable manifolds for invariant Morse function ⋮ Global fixed points for nilpotent actions on the torus ⋮ Fixed points of local actions of nilpotent Lie groups on surfaces ⋮ Rigidity of trivial actions of abelian-by-cyclic groups ⋮ Smooth actions of Lie groups and Lie algebras on manifolds ⋮ Fixed points of nilpotent actions on ⋮ Locally free actions of non-unimodular groups ⋮ Primary singularities of vector fields on surfaces ⋮ Any Baumslag–Solitar action on surfaces with a pseudo-Anosov element has a finite orbit ⋮ Zero sets of Lie algebras of analytic vector fields on real and complex two-dimensional manifolds ⋮ Fixed points for nilpotent actions on the plane and the Cartwright-Littlewood theorem

Cites Work

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• Foliations with measure preserving holonomy
• Regular families of curves
• Common singularities of commuting vector fields on 2-manifolds
• Growth of connected locally compact groups
• Flows on Homogeneous Spaces. (AM-53)
• Introduction to the Geometry of Foliations, Part A
• A global formulation of the Lie theory of transformation groups

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