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Geometriae Dedicata

, Volume 200, Issue 1, pp 385–439 | Cite as

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

  • Kurt Vinhage
  • Zhenqi Jenny WangEmail author
Original Paper
  • 60 Downloads

Abstract

We show local and cocycle rigidity for most abelian higher-rank partially hyperbolic algebraic actions on homogeneous spaces obtained from semisimple Lie groups as well as their semidirect products. The method of proof uses a combination of geometric method and the theory of central extensions. The principal difference with previous work are the new aspects of the proof and treatment of abelian actions which are not restrictions of Weyl chamber flows. It is also the first time that partially hyperbolic twisted symmetric space examples have been treated in the literature.

Keywords

Local rigidity Cocycle rigidity Geometric method Central extension Algebraic K-theory 

Mathematics Subject Classification

37C85 37C15 

Notes

Acknowledgements

The authors would like to thank their mutual advisor Anatole Katok for his introduction of the problem and valuable input and encouragement, as well as Aaron Brown, Ralf Spatzier and Federico Rodriguez-Hertz for helpful discussions on the subject.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA
  2. 2.Department of MathematicsMichigan State UniversityEast LansingUSA

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