1.

Record Nr.

UNINA9910338248103321

Autore

Kim Sang-hyun

Titolo

Flexibility of Group Actions on the Circle / / by Sang-hyun Kim, Thomas Koberda, Mahan Mj

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019

ISBN

3-030-02855-0

Edizione

[1st ed. 2019.]

Descrizione fisica

1 online resource (X, 136 p. 33 illus., 2 illus. in color.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 2231

Disciplina

512.2

512.55

Soggetti

Group theory

Dynamics

Ergodic theory

Manifolds (Mathematics)

Complex manifolds

Algebra

Ordered algebraic structures

Group Theory and Generalizations

Dynamical Systems and Ergodic Theory

Manifolds and Cell Complexes (incl. Diff.Topology)

Order, Lattices, Ordered Algebraic Structures

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

- Introduction -- Preliminaries -- Topological Baumslag Lemmas. - Splittable Fuchsian Groups. - Combination Theorem for Flexible Groups. - Axiomatics. - Mapping Class Groups. - Zero Rotation Spectrum and Teichmüller Theory.

Sommario/riassunto

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.