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Flexiblity of group actions on the c...

Kim, Sang-hyun.

Flexiblity of group actions on the circle

Record Type:	Electronic resources : Monograph/item
Title/Author:	Flexiblity of group actions on the circleby Sang-hyun Kim, Thomas Koberda, Mahan Mj.
Author:	Kim, Sang-hyun.
other author:	Koberda, Thomas.
Published:	Cham :Springer International Publishing :2019.
Description:	x, 136 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Group actions (Mathematics)
Online resource:	https://doi.org/10.1007/978-3-030-02855-8
ISBN:	9783030028558$q(electronic bk.)

Flexiblity of group actions on the circle
Kim, Sang-hyun.

Flexiblity of group actions on the circle[electronic resource] /by Sang-hyun Kim, Thomas Koberda, Mahan Mj. - Cham :Springer International Publishing :2019. - x, 136 p. :ill., digital ;24 cm. - Lecture notes in mathematics,22310075-8434 ;. - Lecture notes in mathematics ;2035..

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

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.

ISBN: 9783030028558$q(electronic bk.)

Standard No.: 10.1007/978-3-030-02855-8doiSubjects--Topical Terms:

245413
Group actions (Mathematics)

LC Class. No.: QA174.2 / .K55 2019

Dewey Class. No.: 512.2

Flexiblity of group actions on the circle
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520 $a 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.
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