Group Actions in Ergodic Theory, Geometry, and Topology

Selected Papers

Robert J. Zimmer

Edited by David Fisher With a Foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis

The University of Chicago Press II Chicago and London The University of Chicago Press, Chicago 60637 The University of Chicago Press, Ltd., London © 2020 by The University of Chicago All rights reserved. No part of this book may be used or reproduced in any manner whatsoever without written permission, except in the case of brief quotations in critical articles and reviews. For more information, contact the University of Chicago Press, 1427 E. 6oth St., Chicago, IL 60637. Published 2020 Printed in the United States of America

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ISBN-13: 978-o-226-56813-3 (cloth) ISBN-13: 978-o-226-56827-o (e-book) DOl: https:/ /doi.org/10.7208/chicago/9780226568270.00I.0001

Library of Congress Cataloging-in-Publication Data

Names: Zimmer, Robert]., 1947- author. I Fisher, David (Mathematician), editor, writer of foreword. I Lubotzky, Alexander, 1956- writer of foreword. I Margulis, G. A. (Gregori Aleksandrovitsch), 1946- writer of foreword. Title: Group actions in ergodic theory, geometry, and topology : selected papers I Robert]. Zimmer; edited by David Fisher; with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis. Description: Chicago ; London : University of Chicago Press, 2020. I Includes bibliographical references. I Contents: Spectra and structure of ergodic actions Amenable actions, equivalence relations, and foliations-Orbit equivalence and strong rigidity-Cocycle superrigidity and the program to describe Lie group and lattice actions on manifolds-Stabilizers of semisimple Lie group actions : invariant random subgroups-Representations and arithmetic properties of actions, fundamental groups, and foliations-Geometric structures : automorphisms of geometric manifolds and rigid structures ; locally homogeneous manifolds Stationary measures and structure theorems for Lie group actions. Identifiers: LCCN 20190309861 ISBN 9780226568133 (cloth) I ISBN 9780226568270 (ebook) Subjects: LCSH: Group actions (Mathematics) I Ergodic theory. I Lie groups. Classification: LCC QA3 .Z56 2020 I DDC 512/.2-dc23 LC record available at https:/ /lccn.loc.gov/2o19030986

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