Groups acting on manifolds: around the Zimmer program

Details Groups acting on manifolds: around the Zimmer program Groups acting on manifolds: around the Zimmer program

2008-09-28

arxiv.org/abs/0809.4849v2

Mathematics

Dynamical Systems

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

Scientific paper

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.

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