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Explore the intricate world of group actions on one-manifolds with ‘Structure and Regularity of Group Actions on One-Manifolds’ from Springer Monographs in Mathematics. This definitive guide delves into optimal and critical regularities, tracing a path from Denjoy and Herman’s foundational work to cutting-edge research. Discover how Filipkiewicz’s Theorem reconstructs manifold structure from its diffeomorphism group, covering topics like homeomorphism group simplicity, Lie group actions, and smooth conjugation. The book examines tools for controlling dynamics of finitely generated group actions, featuring insights on Thompson’s group F, nilpotent groups, and applications in foliation theory and mapping class groups. An essential read for researchers in geometric group theory.
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