LEADER 04021nam 22007335 450 001 9910338248103321 005 20200630064401.0 010 $a3-030-02855-0 024 7 $a10.1007/978-3-030-02855-8 035 $a(CKB)4100000007598344 035 $a(DE-He213)978-3-030-02855-8 035 $a(MiAaPQ)EBC5924830 035 $a(PPN)233797106 035 $a(EXLCZ)994100000007598344 100 $a20190107d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFlexibility of Group Actions on the Circle /$fby Sang-hyun Kim, Thomas Koberda, Mahan Mj 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (X, 136 p. 33 illus., 2 illus. in color.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2231 311 $a3-030-02854-2 320 $aIncludes bibliographical references and index. 327 $a- Introduction -- Preliminaries -- Topological Baumslag Lemmas. - Splittable Fuchsian Groups. - Combination Theorem for Flexible Groups. - Axiomatics. - Mapping Class Groups. - Zero Rotation Spectrum and Teichmüller Theory. 330 $aIn this partly expository work, a framework is developed for building exotic circle actions of certain classical groups. The authors give general combination theorems for indiscrete isometry groups of hyperbolic space which apply to Fuchsian and limit groups. An abundance of integer-valued subadditive defect-one quasimorphisms on these groups follow as a corollary. The main classes of groups considered are limit and Fuchsian groups. Limit groups are shown to admit large collections of faithful actions on the circle with disjoint rotation spectra. For Fuchsian groups, further flexibility results are proved and the existence of non-geometric actions of free and surface groups is established. An account is given of the extant notions of semi-conjugacy, showing they are equivalent. This book is suitable for experts interested in flexibility of representations, and for non-experts wanting an introduction to group representations into circle homeomorphism groups. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2231 606 $aGroup theory 606 $aDynamics 606 $aErgodic theory 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aAlgebra 606 $aOrdered algebraic structures 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 606 $aOrder, Lattices, Ordered Algebraic Structures$3https://scigraph.springernature.com/ontologies/product-market-codes/M11124 615 0$aGroup theory. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aManifolds (Mathematics) 615 0$aComplex manifolds. 615 0$aAlgebra. 615 0$aOrdered algebraic structures. 615 14$aGroup Theory and Generalizations. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aManifolds and Cell Complexes (incl. Diff.Topology). 615 24$aOrder, Lattices, Ordered Algebraic Structures. 676 $a512.2 676 $a512.55 700 $aKim$b Sang-hyun$4aut$4http://id.loc.gov/vocabulary/relators/aut$0691784 702 $aKoberda$b Thomas$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aMj$b Mahan$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910338248103321 996 $aFlexibility of Group Actions on the Circle$92517365 997 $aUNINA