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Flexibility of Group Actions on the Circle

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Flexibility of Group Actions on the Circle/ by Sang-hyun Kim, Thomas Koberda, Mahan Mj.
作者:	Kim, Sang-hyun.
其他作者:	Koberda, Thomas.
面頁冊數:	X, 136 p. 33 illus., 2 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Group theory. -
電子資源:	https://doi.org/10.1007/978-3-030-02855-8
ISBN:	9783030028558

Flexibility of Group Actions on the Circle
Kim, Sang-hyun.

Flexibility of Group Actions on the Circle[electronic resource] /by Sang-hyun Kim, Thomas Koberda, Mahan Mj. - 1st ed. 2019. - X, 136 p. 33 illus., 2 illus. in color.online resource. - Lecture Notes in Mathematics,22310075-8434 ;. - Lecture Notes in Mathematics,2144.

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

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

527791
Group theory.

LC Class. No.: QA174-183

Dewey Class. No.: 512.2

Flexibility of Group Actions on the Circle
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