Ergodic Theory, Groups, and Geometry
by Robert J. Zimmer and Dave Witte Morris

Published in the CBMS Lecture Notes series of the American Mathematical Society (2008).
A paperback hardcopy can be purchased online from:
Click HERE for a PDF file of the entire 95-page book (approx 825K).

Abstract. The study of group actions on manifolds is the meeting ground of a variety of mathematical areas. In particular, interesting geometric insights can be obtained by applying measure theoretic techniques. These notes provide an introduction to some of the important methods, major developments, and open problems in the subject. They are slightly expanded from lectures of R.J.Zimmer at a CBMS Conference at the University of Minnesota, Minneapolis, in June, 1998. The main text presents a perspective on the field as it was at that time, and comments after the notes of each lecture provide suggestions for further reading, including references to recent developments, but the content of these notes is by no means exhaustive.

Table of Contents

Lecture 1. Introduction
Lecture 2. Actions in Dimension 1 or 2
Lecture 3. Geometric Structures
Lecture 4. Fundamental Groups I
Lecture 5. Gromov Representation
Lecture 6. Superrigidity and First Applications
Lecture 7. Fundamental Groups II (Arithmetic Theory)
Lecture 8. Locally Homogeneous Spaces
Lecture 9. Stationary Measures and Projective Quotients
Lecture 10. Orbit Equivalence
Appendix: Background Material