Isotropy Of Semisimple Group Actions On Manifolds With Geometric Structure
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Isotropy of Semisimple Group Actions on Manifolds with Geometric Structure
Author | : John Patrick Szaro |
Publsiher | : Unknown |
Total Pages | : 222 |
Release | : 1997 |
Genre | : Electronic Book |
ISBN | : UOM:39015041112601 |
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Geometry Rigidity and Group Actions
Author | : Robert J Zimmer |
Publsiher | : University of Chicago Press |
Total Pages | : 600 |
Release | : 2011-04-15 |
Genre | : Mathematics |
ISBN | : 9780226237909 |
Download Geometry Rigidity and Group Actions Book in PDF, Epub and Kindle
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.
Structure and Regularity of Group Actions on One Manifolds
Author | : Sang-hyun Kim,Thomas Koberda |
Publsiher | : Springer Nature |
Total Pages | : 323 |
Release | : 2021-11-19 |
Genre | : Mathematics |
ISBN | : 9783030890063 |
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This book presents the theory of optimal and critical regularities of groups of diffeomorphisms, from the classical work of Denjoy and Herman, up through recent advances. Beginning with an investigation of regularity phenomena for single diffeomorphisms, the book goes on to describes a circle of ideas surrounding Filipkiewicz's Theorem, which recovers the smooth structure of a manifold from its full diffeomorphism group. Topics covered include the simplicity of homeomorphism groups, differentiability of continuous Lie group actions, smooth conjugation of diffeomorphism groups, and the reconstruction of spaces from group actions. Various classical and modern tools are developed for controlling the dynamics of general finitely generated group actions on one-dimensional manifolds, subject to regularity bounds, including material on Thompson's group F, nilpotent groups, right-angled Artin groups, chain groups, finitely generated groups with prescribed critical regularities, and applications to foliation theory and the study of mapping class groups. The book will be of interest to researchers in geometric group theory.
Group Actions on Manifolds
Author | : Reinhard Schultz |
Publsiher | : American Mathematical Soc. |
Total Pages | : 586 |
Release | : 1985 |
Genre | : Mathematics |
ISBN | : 9780821850381 |
Download Group Actions on Manifolds Book in PDF, Epub and Kindle
Presents an understanding of the sorts of problems one studies in group actions and the methods used to study such problems. This book features articles based upon lectures at the 1983 AMS-IMS-SIAM Joint Summer Research Conference, Group Actions on Manifolds, held at the University of Colorado.
American Journal of Mathematics
Author | : Anonim |
Publsiher | : Unknown |
Total Pages | : 722 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : UCAL:B4334155 |
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Geometry Rigidity and Group Actions
Author | : Robert J. Zimmer,Benson Farb,David Fisher |
Publsiher | : University of Chicago Press |
Total Pages | : 659 |
Release | : 2011-04-15 |
Genre | : Mathematics |
ISBN | : 9780226237893 |
Download Geometry Rigidity and Group Actions Book in PDF, Epub and Kindle
The study of group actions is more than 100 years old but remains a widely studied topic in a variety of mathematic fields. A central development in the last 50 years is the phenomenon of rigidity, whereby one can classify actions of certain groups. This book looks at rigidity.
Lie Groups and Geometric Aspects of Isometric Actions
Author | : Marcos M. Alexandrino,Renato G. Bettiol |
Publsiher | : Springer |
Total Pages | : 213 |
Release | : 2015-05-22 |
Genre | : Mathematics |
ISBN | : 9783319166131 |
Download Lie Groups and Geometric Aspects of Isometric Actions Book in PDF, Epub and Kindle
This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach. After a gentle introduction to the subject, some of its recent applications to active research areas are explored, keeping a constant connection with the basic material. The topics discussed include polar actions, singular Riemannian foliations, cohomogeneity one actions, and positively curved manifolds with many symmetries. This book stems from the experience gathered by the authors in several lectures along the years and was designed to be as self-contained as possible. It is intended for advanced undergraduates, graduate students and young researchers in geometry and can be used for a one-semester course or independent study.
Geometry of Group Representations
Author | : William Mark Goldman,Andy R. Magid,American Mathematical Society |
Publsiher | : American Mathematical Soc. |
Total Pages | : 330 |
Release | : 1988 |
Genre | : Mathematics |
ISBN | : 9780821850824 |
Download Geometry of Group Representations Book in PDF, Epub and Kindle
Contains papers based on talks delivered at the AMS-IMS-SIAM Summer Research Conference on the Geometry of Group Representations, held at the University of Colorado in Boulder in July 1987. This work offers an understanding of the state of research in the geometry of group representations and their applications.