Recent progress in the Zimmer program

Abstract

This paper can be viewed as a sequel to the author's long survey on the Zimmer program \cite{F11} published in 2011. The sequel focuses on recent rapid progress on certain aspects of the program particularly concerning rigidity of Anosov actions and Zimmer's conjecture that there are no actions in low dimensions. Some emphasis is put on the surprising connections between these two different sets of developments and also on the key connections and ideas for future research that arise from these works taken together.

This is an expository article that will appear in Bob Zimmer's selected papers. Version to appear. I may eventually update this further for more recent developments

References in corpus (2)

• Invariant measures and measurable projective factors for actions of higher-rank lattices on manifolds
• Rigidity and geometricity for surface group actions on the circle

Cited by in corpus (3)

• Superrigidity, arithmeticity, normal subgroups: results, ramifications and directions
• Rigidity theorems for higher rank lattice actions
• Zimmer's conjecture for lattice actions: the $\mathrm{SL}(n,\mathbb{C})$-case