Groups acting on manifolds: around the Zimmer program
Abstract
This paper is a survey on the 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.
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