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:
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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