Volume 10, issue 2 (2006)

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

Geometry & Topology 10 (2006) 929–954
 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