Flexibility of Group Actions on the Circle
In this partly expository work, a framework is developed for building exotic circle actions of certain classical groups. The authors give general combination theorems for indiscrete isometry groups of hyperbolic space which apply to Fuchsian and limit gro
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Sang-hyun Kim Thomas Koberda Mahan Mj
Flexibility of Group Actions on the Circle
Lecture Notes in Mathematics Editors-in-Chief: Jean-Michel Morel, Cachan Bernard Teissier, Paris Advisory Board: Michel Brion, Grenoble Camillo De Lellis, Princeton Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Sang-hyun Kim • Thomas Koberda • Mahan Mj
Flexibility of Group Actions on the Circle
123
Sang-hyun Kim School of Mathematics Korea Institute for Advanced Study Seoul, Republic of Korea
Thomas Koberda Department of Mathematics University of Virginia Charlottesville, VA, USA
Mahan Mj School of Mathematics Tata Institute of Fundamental Research Mumbai, India
ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-3-030-02854-1 ISBN 978-3-030-02855-8 (eBook) https://doi.org/10.1007/978-3-030-02855-8 Library of Congress Control Number: 2018962878 Mathematics Subject Classification (2010): Primary: 57M60, 37E10; Secondary: 57M50, 20F34, 37E45; 20F65, 57S05 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
In this partly expository monograph, we develop a general framework for producing uncountable families of exotic actions of certain classically studied groups acting on the circle. We show that if L is a nontrivial limit group, then the nonlinear representation variety Hom(L, Homeo+ (S 1 )) contains uncountably many semi-conjugacy classes of faithful actions on S 1 with pairwise disjoint rotation spectra (except for
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