Volume 10, issue 2 (2006)

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Global rigidity for totally nonsymplectic Anosov $\mathbb{Z}^k$ actions

Boris Kalinin and Victoria Sadovskaya

Geometry & Topology 10 (2006) 929–954

arXiv: math/0602175

Abstract

We consider a totally nonsymplectic (TNS) Anosov action of k which is either uniformly quasiconformal or pinched on each coarse Lyapunov distribution. We show that such an action on a torus is C–conjugate to an action by affine automorphisms. We also obtain similar global rigidity results for actions on an arbitrary compact manifold assuming that the coarse Lyapunov foliations are topologically jointly integrable.

Keywords
Anosov systems, abelian actions, smooth conjugacy, rigidity
Mathematical Subject Classification 2000
Primary: 37C15, 37D99
Secondary: 58R99
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Publication
Received: 8 September 2005
Accepted: 5 June 2006
Published: 24 July 2006
Proposed: Benson Farb
Seconded: David Gabai, Leonid Polterovich
Authors
Boris Kalinin
Department of Mathematics and Statistics
University of South Alabama
Mobile, AL 36688
USA
Victoria Sadovskaya
Department of Mathematics and Statistics
University of South Alabama
Mobile, AL 36688
USA