LEADER 04610nam 22004215a 450 001 9910151936403321 005 20091109150325.0 010 $a3-03719-529-0 024 70$a10.4171/029 035 $a(CKB)3710000000953811 035 $a(CH-001817-3)55-091109 035 $a(PPN)178167924 035 $a(EXLCZ)993710000000953811 100 $a20091109j20070525 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHandbook of Teichmu?ller Theory, Volume I$b[electronic resource] /$fAthanase Papadopoulos 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2007 215 $a1 online resource (802 pages) 225 0 $aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;$x2523-5133 ;$v11 327 $tIntroduction to Teichmu?ller theory, old and new /$rAthanase Papadopoulos --$tHarmonic maps and Teichmu?ller theory /$rGeorgios D. Daskalopoulos, Richard A. Wentworth --$tOn Teichmu?ller's metric and Thurston's asymmetric metric on Teichmu?ller space /$rAthanase Papadopoulos, Guillaume The?ret --$tSurfaces, circles, and solenoids /$rRobert C. Penner --$tAbout the embedding of Teichmu?ller space in the space of geodesic Ho?lder distributions /$rJean-Pierre Otal --$tTeichmu?ller spaces, triangle groups and Grothendieck dessins /$rWilliam J. Harvey --$tOn the boundary of Teichmu?ller disks in Teichmu?ller and in Schottky space /$rFrank Herrlich, Gabriela Schmithu?sen --$tIntroduction to mapping class groups of surfaces and related groups /$rShigeyuki Morita --$tGeometric survey of subgroups of mapping class groups /$rJohn Loftin --$tDeformations of Kleinian groups /$rAlbert Marden --$tGeometry of the complex of curves and of Teichmu?ller space /$rUrsula Hamensta?dt --$tParameters for generalized Teichmu?ller spaces /$rCharalampos Charitos, Ioannis Papadoperakis --$tOn the moduli space of singular euclidean surfaces /$rMarc Troyanov --$tDiscrete Riemann surfaces /$rChristian Mercat --$tOn quantizing Teichmu?ller and Thurston theories /$rLeonid Chekhov, Robert C. Penner --$tDual Teichmu?ller and lamination spaces /$rVladimir V. Fock, Alexander Goncharov --$tAn analog of a modular functor from quantized Teichmu?ller theory /$rJo?rg Teschner --$tOn quantum moduli space of flat PSL2(?)-connections on a punctured surface /$rRinat Kashaev. 330 $aThe Teichmu?ller space of a surface was introduced by O. Teichmu?ller in the 1930s. It is a basic tool in the study of Riemann's moduli space and of the mapping class group. These objects are fundamental in several fields of mathematics including algebraic geometry, number theory, topology, geometry, and dynamics. The original setting of Teichmu?ller theory is complex analysis. The work of Thurston in the 1970s brought techniques of hyperbolic geometry in the study of Teichmu?ller space and of its asymptotic geometry. Teichmu?ller spaces are also studied from the point of view of the representation theory of the fundamental group of the surface in a Lie group G, most notably G?=?PSL(2,?) and G?=?PSL(2,?). In the 1980s, there evolved an essentially combinatorial treatment of the Teichmu?ller and moduli spaces involving techniques and ideas from high-energy physics, namely from string theory. The current research interests include the quantization of Teichmu?ller space, the Weil-Petersson symplectic and Poisson geometry of this space as well as gauge-theoretic extensions of these structures. The quantization theories can lead to new invariants of hyperbolic 3-manifolds. The purpose of this handbook is to give a panorama of some of the most important aspects of Teichmu?ller theory. The handbook should be useful to specialists in the field, to graduate students, and more generally to mathematicians who want to learn about the subject. All the chapters are self-contained and have a pedagogical character. They are written by leading experts in the subject. 606 $aComplex analysis$2bicssc 606 $aFunctions of a complex variable$2msc 606 $aSeveral complex variables and analytic spaces$2msc 615 07$aComplex analysis 615 07$aFunctions of a complex variable 615 07$aSeveral complex variables and analytic spaces 686 $a30-xx$a32-xx$2msc 702 $aPapadopoulos$b Athanase 801 0$bch0018173 906 $aBOOK 912 $a9910151936403321 996 $aHandbook of Teichmu?ller Theory, Volume I$92564460 997 $aUNINA