Global rigidity for totally nonsymplectic Anosov ℤk actions

Kalinin, Boris; Sadovskaya, Victoria

doi:10.2140/gt.2006.10.929

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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

DOI: 10.2140/gt.2006.10.929

arXiv: math/0602175

Abstract

We consider a totally nonsymplectic (TNS) Anosov action of $ℤ^{k}$ which is either uniformly quasiconformal or pinched on each coarse Lyapunov distribution. We show that such an action on a torus is $C^{\infty}$ –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

Volume 10, issue 2 (2006)