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Flexibility of Group Actions on the ...

Kim, Sang-hyun.

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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.
出版者:	Cham, Switzerland :Springer, : c2019.,
面頁冊數:	x, 136 p. :ill. ;23 cm.
內容註:	Introduction -- Preliminaries -- Topological Baumslag Lemmas -- Splittable Fuchsian Groups -- Combination Theorem for Flexible Groups -- Axiomatics -- Mapping Class Groups -- Zero Rotation Spectrum and Teichmüller Theory.
標題:	Algebra. -
ISBN:	9783030028541

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

Flexibility of Group Actions on the Circle /by Sang-hyun Kim, Thomas Koberda, Mahan Mj. - 1st ed. - Cham, Switzerland :Springer,c2019. - x, 136 p. :ill. ;23 cm. - Lecture Notes in Mathematics,22310075-8434 ;. - Lecture Notes in Mathematics,2231..

Includes bibliographical references (p. 127-131) and index.

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: 9783030028541EUR34.99

LCCN: 2018962878Subjects--Topical Terms:

516203
Algebra.

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

Dewey Class. No.: 512.2

Flexibility of Group Actions on the Circle /
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100 1 $a Kim, Sang-hyun. $3 3470109
245 1 0 $a Flexibility of Group Actions on the Circle / $c by Sang-hyun Kim, Thomas Koberda, Mahan Mj.
250 $a 1st ed.
260 $a Cham, Switzerland : $b Springer, $c c2019.
300 $a x, 136 p. : $b ill. ; $c 23 cm.
490 1 $a Lecture Notes in Mathematics, $x 0075-8434 ; $v 2231
504 $a Includes bibliographical references (p. 127-131) and index.
505 0 $a Introduction -- Preliminaries -- Topological Baumslag Lemmas -- Splittable Fuchsian Groups -- Combination Theorem for Flexible Groups -- Axiomatics -- Mapping Class Groups -- Zero Rotation Spectrum and Teichmüller Theory.
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.
650 0 $a Algebra. $3 516203
650 0 $a Complex manifolds. $3 660495
650 0 $a Dynamics. $3 519830
650 0 $a Ergodic theory. $3 555691
650 0 $a Group theory. $3 523248
650 0 $a Manifolds (Mathematics). $3 734918
650 0 $a Ordered algebraic structures. $3 713880
700 1 $a Koberda, Thomas. $3 3470110
700 1 $a Mj, Mahan. $3 3270929
830 0 $a Lecture Notes in Mathematics, $x 0075-8434 ; $v 2231. $3 3470111