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Flexibility of Group Actions on the Circle

  • Sang-hyun Kim
  • Thomas Koberda
  • Mahan Mj

Part of the Lecture Notes in Mathematics book series (LNM, volume 2231)

Table of contents

  1. Front Matter
    Pages i-x
  2. Sang-hyun Kim, Thomas Koberda, Mahan Mj
    Pages 1-17
  3. Sang-hyun Kim, Thomas Koberda, Mahan Mj
    Pages 19-34
  4. Sang-hyun Kim, Thomas Koberda, Mahan Mj
    Pages 35-44
  5. Sang-hyun Kim, Thomas Koberda, Mahan Mj
    Pages 45-69
  6. Sang-hyun Kim, Thomas Koberda, Mahan Mj
    Pages 71-79
  7. Sang-hyun Kim, Thomas Koberda, Mahan Mj
    Pages 81-92
  8. Sang-hyun Kim, Thomas Koberda, Mahan Mj
    Pages 93-96
  9. Sang-hyun Kim, Thomas Koberda, Mahan Mj
    Pages 97-114
  10. Back Matter
    Pages 115-136

About this book

Introduction

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 groups. An abundance of integer-valued subadditive defect-one quasimorphisms on these groups follow as a corollary.

The main classes of groups considered are limit and Fuchsian groups. Limit groups are shown to admit large collections of faithful actions on the circle with disjoint rotation spectra. For Fuchsian groups, further flexibility results are proved and the existence of non-geometric actions of free and surface groups is established. An account is given of the extant notions of semi-conjugacy, showing they are equivalent.

This book is suitable for experts interested in flexibility of representations, and for non-experts wanting an introduction to group representations into circle homeomorphism groups.


Keywords

Baumslag Lemma Combination Theorems Rotation Spectrum Semi-conjugacy of Group Actions Surface Group Representations

Authors and affiliations

  1. 1.School of Mathematics, Korea Institute for Advanced StudySeoulKorea (Republic of)
  2. 2.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA
  3. 3.School of MathematicsTata Institute of Fundamental ResearchMumbaiIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-02855-8
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-02854-1
  • Online ISBN 978-3-030-02855-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site