Group Actions in Ergodic Theory, Geometry, and Topology : Selected Papers /

Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer, which lay out his program and contextualize h...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Zimmer, Robert J. (Autor, Contribuidor)
Otros Autores: Fisher, David (Contribuidor, Editor ), Katok, A. (Contribuidor), Labourie, F. (Contribuidor), Labourie, Franqois (Contribuidor), Lashof, Richard K. (Contribuidor), Lewis, J. (Contribuidor), Lubotzky, Alexander (Contribuidor), Margulis, Gregory (Contribuidor), Mozes, S. (Contribuidor), Nevo, Amos (Contribuidor), Spatzier, Ralf J. (Contribuidor), Stuck, Garrett (Contribuidor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Chicago : University of Chicago Press, [2020]
Temas:
Ergodic theory.
Group actions (Mathematics)
Group actions (Mathematics).
Group actions.
Lie groups.
MATHEMATICS / General.
math, mathematics, science, topology, arithmetic groups, dynamical systems, differential geometry, lie theory, ergodic group, cocycle superrigidity theorem, generalized discrete spectrum, orbit spaces, foliations, amenable actions, equivalence relations, hyperfinite factors, curvature, rigidity, lattices, negatively curved manifolds, ratners, nonfiction.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Frontmatter
  • Contents
  • Foreword
  • INTRODUCTION
  • 1. Spectra and Structure of Ergodic Actions
  • A. Extensions of Ergodic Group Actions
  • B. Ergodic Actions with Generalized Discrete Spectrum
  • C. Orbit Spaces of Unitary Representations, Ergodic Theory, and Simple Lie Groups
  • 2 Amenable Actions, Equivalence Relations, and Foliations
  • A. Amenable Ergodic Group Actions and an Application to Poisson Boundaries of Random Walks
  • B. Induced and Amenable Ergodic Actions of Lie Groups
  • C. Hyperfinite Factors and Amenable Ergodic Actions, Inventiones mathematicae (1977)
  • D. Curvature of Leaves in Amenable Foliations, American journal of Mathematics (1983)
  • E. Amenable Actions and Dense Subgroups of Lie Groups Journal of Functional Analysis (1987)
  • 3 Orbit Equivalence and Strong Rigidity
  • A. Strong Rigidity for Ergodic Actions of Semisimple Lie Groups, Annals of Mathematics (1980)
  • B. Orbit Equivalence and Rigidity of Ergodic Actions of Lie Groups
  • C. Ergodic Actions of Semisimple Groups and Product Relations
  • 4 Cocycle Superrigidity and the Program to Describe Lie Group and Lattice Actions on Manifolds
  • A. Volume Preserving Actions of Lattices in Semisimple Groups on Compact Manifolds, Institut des Hautes Etudes Scientifiques Publications Mathematiques (1984)
  • B. Kazhdan Groups Acting on Compact Manifolds, Inventiones mathematicae (1984)
  • C. Actions of Lattices in Semisimple Groups Preserving a G-Structure of Finite Type, Ergodic Theory and Dynamical Systems (1985)
  • D. Actions of Semisimple Groups and Discrete Subgroups, Proceedings of the International Congress of Mathematicians, August 3-11, 1986 (1987)
  • E. Split Rank and Semisimple Automorphism Groups of G-Structures, journal of Differential Geometry (1987)
  • F. Manifolds with Infinitely Many Actions of an Arithmetic Group
  • G. Spectrum, Entropy, and Geometric Structures for Smooth Actions of Kazhdan Groups
  • H. Cocycle Superrigidity and Rigidity for Lattice Actions on Tori (with Anatole Katok and James Lewis)
  • I. Volume-Preserving Actions of Simple Algebraic Q-Groups on Low-Dimensional Manifolds (with Dave Witte Morris)
  • 5 Stabilizers of Semisimple Lie Group Actions: Invariant Random Subgroups
  • A. Stabilizers for Ergodic Actions of Higher Rank Semisimple Groups (with Garrett Stuck)
  • 6 Representations and Arithmetic Properties of Actions, Fundamental Groups, and Foliations
  • A. Arithmeticity ofHolonomy Groups of Lie Foliations
  • B. Representations of Fundamental Groups of Manifolds with a Semisimple Transformation Group
  • C. Superrigidity, Ratner's Theorem, and Fundamental Groups
  • D. Fundamental Groups of Negatively Curved Manifolds and Actions of Semi simple Groups
  • A canonical arithmetic quotient for simple Lie group actions
  • F. A Canonical Arithmetic Quotient for Simple Lie Group Actions
  • G. Entropy and Arithmetic Quotients for Simple Automorphism Groups of Geometric Manifolds
  • H. Geometric Lattice Actions, Entropy and Fundamental Groups
  • 7 Geometric Structures: Automorphisms of Geometric Manifolds and Rigid Structures; Locally Homogeneous Manifolds
  • A. On the Automorphism Group of a Compact Lorentz Manifold and Other Geometric Manifolds
  • B. Semisimple Automorphism Groups of G-Structures
  • C. Automorphism Groups and Fundamental Groups of Geometric Manifolds
  • D. Discrete Groups and Non-Riemannian Homogeneous Spaces
  • E. On Manifolds Locally Modelled on Non-Riemannian Homogeneous Spaces
  • F. On the Non-existence of Cocompact Lattices for SL(n)!SL(m)
  • 8 Stationary Measures and Structure Theorems for Lie Group Actions
  • A. A Structure Theorem for Actions of Semisimple Lie Groups
  • B. Entropy of Stationary Measures and Bounded Tangential de-Rham Cohomology of Semisimple Lie Group Actions
  • C. Invariant Rigid Geometric Structures and Smooth Projective Factors
  • GROUPS ACTING ON MANIFOLDS: Around the Zimmer Program
  • AFTERWORD: Recent Progress in the Zimmer Program
  • Acknowledgments

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