Groups acting on manifolds: around the Zimmer program

Abstract

This paper is a survey on the {\em Zimmer program}. In it's broadest form, this program seeks an understanding of actions of large groups on compact manifolds. The goals of this survey are $(1)$ to put in context the original questions and conjectures of Zimmer and Gromov that motivated the program, $(2)$ to indicate the current state of the art on as many of these conjectures and questions as possible and $(3)$ to indicate a wide variety of open problems and directions of research.

Survey article, 84 pages, almost final version, comments welcome but only if made quickly

References in corpus (3)

• Mapping Class Groups do not have Kazhdan's Property (T)
• Group actions and Helly's theorem
• Meromorphic almost rigid geometric structures

Cited by in corpus (1)

• Holomorphic actions of higher rank lattices in dimension three