Thomas Koberda's Books

Structure and Regularity of Group Actions on One-Manifolds

By: Sang-hyun Kim,Thomas Koberda

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Structure and Regularity of Group Actions on One-Manifolds

By: Sang-hyun Kim,Thomas Koberda

This book presents the theory of optimal and critical regularities of groups of diffeomorphisms, from the classical work of Denjoy and Herman, up through recent advances. Beginning with an investigation of regularity phenomena for single diffeomorphisms, the book goes on to describes a circle of ideas surrounding Filipkiewicz's Theorem, which recovers the smooth structure of a manifold from its full diffeomorphism group. Topics covered include the simplicity of homeomorphism groups, differentiability of continuous Lie group actions, smooth conjugation of diffeomorphism groups, and the reconstruction of spaces from group actions. Various classical and modern tools are developed for controlling the dynamics of general finitely generated group actions on one-dimensional manifolds, subject to regularity bounds, including material on Thompson's group F, nilpotent groups, right-angled Artin groups, chain groups, finitely generated groups with prescribed critical regularities, and applications to foliation theory and the study of mapping class groups. The book will be of interest to researchers in geometric group theory.

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Page Count

323

Publisher

Springer Nature

Published Date

ISBN 10

3030890066

ISBN 13

9783030890063

Flexibility of Group Actions on the Circle

By: Sang-hyun Kim,Thomas Koberda,Mahan Mj

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Flexibility of Group Actions on the Circle

By: Sang-hyun Kim,Thomas Koberda,Mahan Mj

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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Page Count

140

Publisher

Springer

Published Date

ISBN 10

3030028550

ISBN 13

9783030028558

Structure and Regularity of Group Actions on One-Manifolds

By: Sang-hyun Kim,Thomas Koberda

Write a review Read reviews Take a Quiz Solve Book Puzzle

Structure and Regularity of Group Actions on One-Manifolds

By: Sang-hyun Kim,Thomas Koberda

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

323

Publisher

Springer Nature

Published Date

ISBN 10

3030890066

ISBN 13

9783030890063

Flexibility of Group Actions on the Circle

By: Sang-hyun Kim,Thomas Koberda,Mahan Mj

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Flexibility of Group Actions on the Circle

By: Sang-hyun Kim,Thomas Koberda,Mahan Mj

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

140

Publisher

Springer

Published Date

ISBN 10

3030028550

ISBN 13

9783030028558

Book's by Thomas Koberda

Structure and Regularity of Group Actions on One-Manifolds

Structure and Regularity of Group Actions on One-Manifolds

Flexibility of Group Actions on the Circle

Flexibility of Group Actions on the Circle

Structure and Regularity of Group Actions on One-Manifolds

Structure and Regularity of Group Actions on One-Manifolds

Flexibility of Group Actions on the Circle

Flexibility of Group Actions on the Circle

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