Local rigidity of higher rank homogeneous abelian actions: a complete solution via the geometric method

DOI10.1007/s10711-018-0379-5zbMath1427.22013arXiv1510.00848OpenAlexW2962907338WikidataQ129439191 ScholiaQ129439191MaRDI QIDQ2417672

Kurt Vinhage, Zhenqi Jenny Wang

Publication date: 12 June 2019

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.00848

zbMATH Keywords

algebraic K-theorycentral extensionlocal rigiditycocycle rigiditygeometric method

Mathematics Subject Classification ID

Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Semisimple Lie groups and their representations (22E46) Rigidity results (53C24) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Obstructions to group actions ((K)-theoretic aspects) (19J35) Central extensions and Schur multipliers (19C09)

Related Items (5)

On simultaneous linearization of certain commuting nearly integrable diffeomorphisms of the cylinder ⋮ Rigidity properties for some isometric extensions of partially hyperbolic actions on the torus ⋮ Cocycle rigidity of partially hyperbolic abelian actions with almost rank-one factors ⋮ Pathology and asymmetry: centralizer rigidity for partially hyperbolic diffeomorphisms ⋮ Transversal local rigidity of discrete abelian actions on Heisenberg nilmanifolds

Cites Work

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• Hölder foliations, revisited
• Global rigidity of higher rank abelian Anosov algebraic actions
• On the rigidity of Weyl chamber flows and Schur multipliers as topological groups
• Local rigidity of partially hyperbolic actions I. KAM method and \({\mathbb Z^k}\) actions on the torus
• New cases of differentiable rigidity for partially hyperbolic actions: symplectic groups and resonance directions
• Local rigidity of homogeneous parabolic actions: I. A model case
• Normal forms and invariant geometric structures for dynamical systems with invariant contracting foliations
• Local rigidity for certain groups of toral automorphisms
• First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity
• Global smooth and topological rigidity of hyperbolic lattice actions
• Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions
• Cocycles' stability for partially hyperbolic systems
• On the classification of Cartan actions
• Central extensions of simple Lie groups and rigidity of some Abelian partially hyperbolic algebraic actions
• Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic \(\mathbb R^k\) actions
• Rigidity of weakly hyperbolic actions of higher real rank semisimple Lie groups and their lattices
• Local Rigidity of Partially Hyperbolic Actions. II: The Geometric Method and Restrictions of Weyl Chamber Flows on SL(n, R)/
• On a Class of Transformation Groups
• Differential Rigidity of Anosov Actions of Higher Rank Abelian Groups and Algebraic Lattice Actions
• On Central Extensions of Rational Points of Algebraic Groups
• Index of the Exponential Map of a Semi-Algebraic Group
• Local rigidity of actions of higher rank abelian groups and KAM method
• Free Products of Topological Groups Which are k ω -Spaces
• Global rigidity of higher rank Anosov actions on tori and nilmanifolds
• Non-abelian cohomology of abelian Anosov actions
• Free products of topological groups
• Introduction to Algebraic K-Theory. (AM-72)
• Invariant manifolds
• Local rigidity of partially hyperbolic actions

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