On the classification of cartan actions

Boris Kalinin; Ralf Spatzier

doi:10.1007/s00039-007-0602-2

On the classification of cartan actions

Boris Kalinin, Ralf Spatzier

Research output: Contribution to journal › Article › peer-review

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Abstract

We study higher-rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by script R sign^k with k ≥ 3 whose one-parameter groups act transitively as well as nondegenerate totally nonsymplectic ℤ^k-actions for k ≥ 3.

Original language	English (US)
Pages (from-to)	468-490
Number of pages	23
Journal	Geometric and Functional Analysis
Volume	17
Issue number	2
DOIs	https://doi.org/10.1007/s00039-007-0602-2
State	Published - Jun 2007

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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title = "On the classification of cartan actions",

abstract = "We study higher-rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by script R signk with k ≥ 3 whose one-parameter groups act transitively as well as nondegenerate totally nonsymplectic ℤk-actions for k ≥ 3.",

author = "Boris Kalinin and Ralf Spatzier",

note = "Funding Information: Keywords and phrases: Hyperbolic dynamics, Anosov actions, rigidity AMS Mathematics Subject Classification: 37D20, 37C85, 58D05 The first author is supported in part by NSF grants DMS-0140513. author is supported in part by NSF grant DMS-0203735.",

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PY - 2007/6

Y1 - 2007/6

N2 - We study higher-rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by script R signk with k ≥ 3 whose one-parameter groups act transitively as well as nondegenerate totally nonsymplectic ℤk-actions for k ≥ 3.

AB - We study higher-rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by script R signk with k ≥ 3 whose one-parameter groups act transitively as well as nondegenerate totally nonsymplectic ℤk-actions for k ≥ 3.

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On the classification of cartan actions

Abstract

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