Local rigidity of partially hyperbolic actions

Zhenqi Jenny Wang

doi:10.3934/jmd.2010.4.271

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2010, Volume 4, Issue 2: 271-327. Doi: 10.3934/jmd.2010.4.271

This issue Previous Article Generating product systems Next Article Spectral invariants in Rabinowitz-Floer homology and global Hamiltonian perturbations

Local rigidity of partially hyperbolic actions

Zhenqi Jenny Wang^1,

1.
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802

Received: September 30, 2009

Revised: May 31, 2010

Published: July 2010

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Abstract

We consider partially hyperbolic abelian algebraic high-rank actions on compact homogeneous spaces obtained from simple indefinite orthogonal and unitary groups. In the first part of the paper, we show local differentiable rigidity for such actions. The conclusions are based on progress toward computations of the Schur multipliers of these non-split groups, which is the main aim of the second part.

Keywords:

action of higher rank abelian groups,
cocycles,
rigidity,
Steinberg symbols,
generators and relations in classical Lie groups.

Mathematics Subject Classification: Primary: 37D; Secondary: 19C, 22E.

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