Compact forms of homogeneous spaces and higher-rank semisimple group actions

David Constantine

Compact forms of homogeneous spaces and higher-rank semisimple group actions

Differential Geometry 2016-06-13 v2 Dynamical Systems

Authors: David Constantine

Abstract

This paper proves that there are no compact forms for a large class of homogeneous spaces admitting actions by higher-rank semisimple Lie groups. It builds on Zimmer's approach for studying such spaces using cocycle superrigidity. The proof involves cocycle superrigidity, measure rigidity for unipotent flows, techniques from partially hyperbolic dynamics, and the geometry and pseudo-Riemannian structure of the homogeneous space.

Keywords

homogeneous spaces compact forms semisimple Lie groups cocycle superrigidity measure rigidity unipotent flows partially hyperbolic dynamics pseudo-Riemannian geometry

Cite

@article{arxiv.1209.3940,
  title  = {Compact forms of homogeneous spaces and higher-rank semisimple group actions},
  author = {David Constantine},
  journal= {arXiv preprint arXiv:1209.3940},
  year   = {2016}
}

Comments

This paper has been withdrawn by the author because of an error in the proof of the main theorem

Compact forms of homogeneous spaces and higher-rank semisimple group actions

Abstract

Keywords

Cite

Comments

Related papers