Volume 10, issue 2 (2006)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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
References
Forward citations
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