The study of group actions is more than a hundred years old but remains to this day a vibrant and widely studied topic in a variety of mathematic fields. A central development in the last fifty years is the phenomenon of rigidity, whereby one can classify actions of certain groups, such as lattices in semi-simple Lie groups. This provides a way to classify all possible symmetries of important spaces and all spaces admitting given symmetries. Paradigmatic results can be found in the seminal work of George Mostow, Gergory Margulis, and Robert J. Zimmer, among others. The papers in Geometry, Rigidity, and Group Actions explore the role of group actions and rigidity in several areas of mathematics, including ergodic theory, dynamics, geometry, topology, and the algebraic properties of representation varieties. In some cases, the dynamics of the possible group actions are the principal focus of inquiry. In other cases, the dynamics of group actions are a tool for proving theorems about algebra, geometry, or topology. This volume contains surveys of some of the main directions in the field, as well as research articles on topics of current interest.
Author(s): Farb B., Fisher D. (eds.)
Series: Chicago Lectures in Mathematics
Publisher: Chicago univ.
Year: 2011
Language: English
Pages: 659
Tags: Математика;Общая алгебра;
Contents
......Page 8
Preface
......Page 10
Part 1: Group Actions on Manifolds
......Page 14
1. An Extension Criterion for Lattice Actions on the Circle / Marc Burger
......Page 16
2. Meromorphic Almost Rigid Geometric Structures / Sorin Dumitrescu
......Page 45
3. Harmonic Functions over Group Actions / Renato Feres and Emily Ronshausen
......Page 72
4. Groups Acting on Manifolds: Around the Zimmer Program / David Fisher
......Page 85
5. Can Lattices in SL (n, R) Act on the Circle? / Dave Witte Morris
......Page 171
6. Some Remarks on Area-Preserving Actions on Lattices / Pierre Py
......Page 221
7. Isometric Actions of Simple Groups and Transverse Structures: The Integrable Normal Case / Raul Quiroga-Barranco
......Page 242
8. Some Remarks Inspired by the CO Zimmer Program / Shmuel Weinberger
......Page 275
Part 2: Analytic, Ergodic, and Measurable Group Theory
......Page 296
9. Calculus on Nilpotent Lie Groups / Michael G. Cowling
......Page 298
10. A Survery of Measured Group Theory / Alex Furman
......Page 309
11. On Relative Property (T) / Alessandra Iozzi
......Page 388
12. Noncommutative Ergodic Theorems / Anders Karlsson and Francois Ledrappier
......Page 409
13. Cocycle and Orbit Superrigidity for Lattices in SL (n, R) Acting on Homogeneous Spaces / Sorin Popa and Stefaan Vaes
......Page 432
Part 3: Geometric Group Theory
......Page 466
14. Heights on SL2 and Free Subgroups / Emmanuel Breuillard
......Page 468
15. Displacing Representations and Orbit Maps / Thomas Delzant, Olivier Guichard, Francois Labourie, and Shahar Mozes
......Page 507
16. Problems on Automorphism Groups of Nonpositively Curved Polyhedral Complexes and Their Lattices / Benson Farb, Chris Hruska, and Anne Thomas
......Page 528
17. The Geometry of Twisted Conjugacy Classes in Wreath Products / Jennifer Taback and Peter Wong
......Page 574
Part 4: Group Actions on Representations Varieties
......Page 602
18. Ergodicity of Mapping Class Group Actions on Su (2)-Character Varieties / William M. Goldman and Eugene Z. Xia
......Page 604
19. Dynamics of Aut (Fn) Actions on Group Presentations and Representations / Alexander Lubotzky
......Page 622
List of Contributors
......Page 658
