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Groups of Circle Diffeomorphisms.

Author: Andrés Navas; Andreś Navas
Publisher: Chicago, IL : University of Chicago Press, 2011.
Series: Chicago lectures in mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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,  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Navas, Andrés.
Groups of Circle Diffeomorphisms.
Chicago, IL : University of Chicago Press, ©2011
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Andrés Navas; Andreś Navas
ISBN: 9780226569505 0226569500 9780226569512 0226569519 1283362732 9781283362733
OCLC Number: 772845711
Description: 1 online resource (310 pages).
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 Diffeomorphisms4. 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 GroupsReferences; Index.
Series Title: Chicago lectures in mathematics.

Abstract:

Group actions are an efficient way of describing symmetries in objects by defining the essential elements of a given object as a set. The symmetries of the object are then defined as the symmetry  Read more...

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"Groups of Circle Diffeomorphisms provides a great overview of the research on differentiable group actions on the circle. Navas's book will appeal to those doing research on differential topology, Read more...

 
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