EAN: 9783030028541

FLEXIBILITY OF GROUP ACTIONS ON THE CIRCLE - SA...

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.

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