Geometry, Rigidity, and Group Actions

Benson Farb

ISBN 10: 0226237885 / ISBN 13: 9780226237886

Published by The University of Chicago Press, US, 2011

About this Item

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, Gregory 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.

Seller Inventory # LU-9780226237886

Bibliographic Details

• Title: Geometry, Rigidity, and Group Actions
• Publisher: The University of Chicago Press, US
• Publication Date: 2011
• Language: English
• ISBN 10: 0226237885
• ISBN 13: 9780226237886
• Binding: Hardback
• Condition: New
• Weight: 1021 grams

About this title

Synopsis

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.

About the Author

David Fisher is the Ruth N. Halls Distinguished Professor of Mathematics at Indiana University, Bloomington.