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Structure and Regularity of Group Actions on One-Manifolds (Hardcover, 1st ed. 2021)
Loot Price: R3,768
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Structure and Regularity of Group Actions on One-Manifolds (Hardcover, 1st ed. 2021)
Series: Springer Monographs in Mathematics
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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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