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  1. Bog
  2. Matematik
  3. Algebra

Structure and Regularity of Group Actions on One-Manifolds

Af: Sang-hyun Kim, Thomas Koberda Engelsk Paperback

Structure and Regularity of Group Actions on One-Manifolds

Af: Sang-hyun Kim, Thomas Koberda Engelsk Paperback
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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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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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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 323
ISBN-13: 9783030890087
Indbinding: Paperback
Udgave:
ISBN-10: 3030890082
Kategori: Algebra
Udg. Dato: 21 nov 2022
Længde: 0mm
Bredde: 155mm
Højde: 235mm
Forlag: Springer Nature Switzerland AG
Oplagsdato: 21 nov 2022
Forfatter(e): Sang-hyun Kim, Thomas Koberda
Forfatter(e) Sang-hyun Kim, Thomas Koberda

Kategori Algebra

ISBN-13 9783030890087

Sprog Engelsk

Indbinding Paperback

Sider 323

Udgave

Længde 0mm

Bredde 155mm

Højde 235mm

Udg. Dato 21 nov 2022

Oplagsdato 21 nov 2022

Forlag Springer Nature Switzerland AG

Kategori sammenhænge