LEADER 03389nam 2200613 a 450 001 9910437864503321 005 20200520144314.0 010 $a1-283-90968-5 010 $a3-0348-0481-4 024 7 $a10.1007/978-3-0348-0481-3 035 $a(CKB)2670000000279901 035 $a(EBL)1082167 035 $a(OCoLC)821020899 035 $a(SSID)ssj0000798458 035 $a(PQKBManifestationID)11427337 035 $a(PQKBTitleCode)TC0000798458 035 $a(PQKBWorkID)10744045 035 $a(PQKB)10926339 035 $a(DE-He213)978-3-0348-0481-3 035 $a(MiAaPQ)EBC1082167 035 $a(PPN)168307324 035 $a(EXLCZ)992670000000279901 100 $a20121009d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aComplex Kleinian groups /$fAngel Cano, Juan Pablo Navarrete, Jose Seade 205 $a1st ed. 2013. 210 $aNew York $cSpringer$d2013 215 $a1 online resource (287 p.) 225 1 $aProgress in mathematics ;$vv. 303 300 $aDescription based upon print version of record. 311 $a3-0348-0805-4 311 $a3-0348-0480-6 320 $aIncludes bibliographical references and index. 327 $a  Preface -- Introduction -- Acknowledgments -- 1 A glance of the classical theory -- 2 Complex hyperbolic geometry -- 3 Complex Kleinian groups -- 4 Geometry and dynamics of automorphisms of P2C -- 5 Kleinian groups with a control group -- 6 The limit set in dimension two -- 7 On the dynamics of discrete subgroups of PU(n,1) -- 8 Projective orbifolds and dynamics in dimension two -- 9 Complex Schottky groups -- 10 Kleinian groups and twistor theory -- Bibliography -- Index.  . 330 $aThis monograph lays down the foundations of the theory of complex Kleinian groups, a ?newborn? area of mathematics whose origin can be traced back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can themselves be regarded as groups of holomorphic automorphisms of the complex projective line CP1. When we go into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere? or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories differ in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition; in the second, about an area of mathematics that is still in its infancy, and this is the focus of study in this monograph. It brings together several important areas of mathematics, e.g. classical Kleinian group actions, complex hyperbolic geometry, crystallographic groups and the uniformization problem for complex manifolds. 410 0$aProgress in mathematics (Boston, Mass.) ;$vv. 303. 606 $aKleinian groups 615 0$aKleinian groups. 676 $a512.2 676 $a512.2 700 $aCano$b Angel$0521830 701 $aNavarrete$b Juan Pablo$0521831 701 $aSeade$b Jose$0368369 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910437864503321 996 $aComplex Kleinian groups$9838165 997 $aUNINA