Groups of Circle Diffeomorphisms
1st Edition
Published on 1. June 2011
310 pages
978-0-226-56950-5 (ISBN)
Description
In recent years scholars from a variety of branches of mathematics have made several significant developments in the theory of group actions. Groups of Circle Diffeomorphisms systematically explores group actions on the simplest closed manifold, the circle. As the group of circle diffeomorphisms is an important subject in modern mathematics, this book will be of interest to those doing research in group theory, dynamical systems, low dimensional geometry and topology, and foliation theory. The book is mostly self-contained and also includes numerous complementary exercises, making it an excellent textbook for undergraduate and graduate students.
More details
Other editions
Additional editions
Andres Navas
Groups of Circle Diffeomorphisms
Book
06/2011
University of Chicago Press
€55.71
Shipment within 10-20 days
Content
- Intro
- Contents
- Introduction
- Acknowledgments
- Notation and General Definitions
- 1. Examples of Group Actions on the Circle
- 1.1 The Group of Rotations
- 1.2 The Group of Translations and the Affine Group
- 1.3 The Group PSL
- 1.4 Actions of Lie Groups
- 1.5 Thompson's Groups
- 2. Dynamics of Groups of Homeomorphisms
- 2.1 Minimal Invariant Sets
- 2.2 Some Combinatorial Results
- 2.3 Invariant Measures and Free Groups
- 3. Dynamics of Groups of Diffeomorphisms
- 3.1 Denjoy's Theorem
- 3.2 Sacksteder's Theorem
- 3.3 Duminy's First Theorem
- 3.4 Duminy's Second Theorem
- 3.5 Two Open Problems
- 3.6 On the Smoothness of the Conjugacy between Groups of Diffeomorphisms
- 4. Structure and Rigidity via Dynamical Methods
- 4.1 Abelian Groups of Diffeomorphisms
- 4.2 Nilpotent Groups of Diffeomorphisms
- 4.3 Polycyclic Groups of Diffeomorphisms
- 4.4 Solvable Groups of Diffeomorphisms
- 4.5 On the Smooth Actions of Amenable Groups
- 5. Rigidity via Cohomological Methods
- 5.1 Thurston's Stability Theorem
- 5.2 Rigidity for Groups with Kazhdan's Property (T)
- 5.3 Superrigidity for Higher-Rank Lattice Actions
- Appendix A: Some Basic Concepts in Group Theory
- Appendix B: Invariant Measures and Amenable Groups
- References
- Index
