TY  - BOOK
AU  - Kim,Sang-hyun
AU  - Koberda,Thomas
AU  - Mj,Mahan
ED  - SpringerLink (Online service)
TI  - Flexibility of Group Actions on the Circle
T2  - Lecture Notes in Mathematics,
SN  - 9783030028558
AV  - QA174-183 
U1  - 512.2 23
PY  - 2019///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Group theory
KW  - Dynamics
KW  - Ergodic theory
KW  - Manifolds (Mathematics)
KW  - Complex manifolds
KW  - Algebra
KW  - Ordered algebraic structures
KW  - Group Theory and Generalizations
KW  - Dynamical Systems and Ergodic Theory
KW  - Manifolds and Cell Complexes (incl. Diff.Topology)
KW  - Order, Lattices, Ordered Algebraic Structures
N1  - - Introduction -- Preliminaries -- Topological Baumslag Lemmas. - Splittable Fuchsian Groups. - Combination Theorem for Flexible Groups. - Axiomatics. - Mapping Class Groups. - Zero Rotation Spectrum and Teichmüller Theory
N2  - 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
UR  - https://doi.org/10.1007/978-3-030-02855-8
ER  -