Flexibility Of Group Actions On The Circle
Download Flexibility Of Group Actions On The Circle PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Flexibility Of Group Actions On The Circle book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Flexibility of Group Actions on the Circle
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.
Structure and Regularity of Group Actions on One-Manifolds
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.
High Impact Practices with Urban Youth--Circles at the Center
Author: Yan Dominic Searcy
language: en
Publisher: Oxford University Press
Release Date: 2023-10-31
High impact practices are evidence-based educational practices that have been shown to increase student learning and raise levels of performance, retention, and success. The circle--commonly known as a discussion circle--is a key high impact practice linked to positive outcomes for urban youth. Circles are effective tools for enhancing communication, promoting emotional support and healing, and encouraging problem-solving and creativity. In High Impact Practices with Urban Youth--Circles at the Center: A Guidebook for Practitioners and Scholar-Activists, Yan Dominic Searcy and Troy Harden provide research-based best practices in an accessible format to bridge the gap between practitioners and researchers who are specifically working to improve the life outcomes of urban youth. Targeted to assist front-line practitioners, program directors, and those training to be practitioners, this book reflects Searcy and Harden's combined over five decades of work with urban youth and imparts high impact practices to influence interventions and program design. Each chapter begins with a brief narrative from a discussion circle, reflective of the authors' interactions with youth or program staff that is germane to a high impact practice. The best youth work combines art and science, emotion and skill. High Impact Practices with Urban Youth effectively blends both to ground the next generation of interventions aimed at improving youth program outcomes whether the programs are targeting juvenile justice, health promotion, education, sports, leadership, or mentoring.