LEADER 04678nam 22004095a 450 001 9910153279403321 005 20160524234501.0 010 $a3-03719-661-0 024 70$a10.4171/161 035 $a(CKB)3340000000002770 035 $a(CH-001817-3)202-160524 035 $a(PPN)193819724 035 $a(EXLCZ)993340000000002770 100 $a20160524j20160531 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 VI$b[electronic resource] /$fAthanase Papadopoulos 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2016 215 $a1 online resource (652 pages) 225 0 $aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;$x2523-5133 ;$v27 311 $a3-03719-161-9 327 $tIntroduction to Teichmu?ller theory, old and new, VI /$rAthanase Papadopoulos --$tAlexander Grothendieck /$rValentin Poe?naru --$tOn Grothendieck's construction of Teichmu?ller space /$rNorbert A'Campo, Lizhen Ji, Athanase Papadopoulos --$tNull-set compactifications of Teichmu?ller spaces /$rVincent Alberge, Hideki Miyachi, Ken'ichi Ohshika --$tMirzakhani's recursion formula on Weil-Petersson volume and applications /$rYi Huang --$tRigidity phenomena in the mapping class group /$rJavier Aramayona, Juan Souto --$tHarmonic volume and its applications /$rYuuki Tadokoro --$tTorus bundles and 2-forms on the universal family of Riemann surfaces /$rRobin de Jong --$tCubic Differentials in the Differential Geometry of Surfaces /$rJohn Loftin, Ian McIntosh --$tTwo-generator groups acting on the complex hyperbolic plane /$rPierre Will --$tConfiguration spaces of planar linkages /$rAlexey Sossinsky --$tQuasiconformal mappings on the Heisenberg group: An overview /$rIoannis D. Platis --$tActions of the absolute Galois group /$rNorbert A'Campo, Lizhen Ji, Athanase Papadopoulos --$tA primer on dessins /$rPierre Guillot --$tHypergeometric Galois Actions /$rA. Muhammed Uludag?, I?smail Sag?lam --$tA panaroma of the fundamental group of the modular orbifold /$rA. Muhammed Uludag?, Ayberk Zeytin --$tOn Grothendieck's tame topology /$rNorbert A'Campo, Lizhen Ji, Athanase Papadopoulos --$tSome historical commentaries on Teichmu?ller's paper Extremale quasikonforme Abbildungen und quadratische Differentiale /$rReiner Ku?hnau --$tComplete solution of an extremal problem of the quasiconformal mapping /$rOswald Teichmu?ller --$tA Commentary on Teichmu?ller's paper Vollsta?ndige Lo?sung einer Extremalaufgabe der quasikonformen Abbildung /$rVincent Alberge, Athanase Papadopoulos --$tOn extremal problems of conformal geometry /$rOswald Teichmu?ller --$tA Commentary on Teichmu?ller's paper U?ber Extremalprobleme der konformen Geometrie /$rNorbert A'Campo, Athanase Papadopoulos --$tA displacement theorem of quasiconformal mapping /$rOswald Teichmu?ller --$tA Commentary on Teichmu?ller's paper Ein Verschiebungssatz der quasikonformen Abbildung /$rVincent Alberge. 330 $aThis volume is the sixth in a series dedicated to Teichmu?ller theory in a broad sense, including various moduli and deformation spaces, and the study of mapping class groups. It is divided into five parts: Part A: The metric and the analytic theory. Part B: The group theory. Part C: Representation theory and generalized structures. Part D: The Grothendieck-Teichmu?ller theory. Part D: Sources. The topics surveyed include Grothendieck's construction of the analytic structure of Teichmu?ller space, identities on the geodesic length spectrum of hyperbolic surfaces (including Mirzakhani's application to the computation of Weil-Petersson volumes), moduli spaces of configurations spaces, the Teichmu?ller tower with the action of the Galois group on dessins d'enfants, and several others actions related to surfaces. The last part contains three papers by Teichmu?ller, translated into English with mathematical commentaries, and a document that contains H. Gro?tzsch's comments on Teichmu?ller's famous paper Extremale quasikonforme Abbildungen und quadratische Differentiale. The handbook is addressed to researchers and to graduate students. 606 $aFunctional analysis$2bicssc 606 $aFunctions of a complex variable$2msc 615 07$aFunctional analysis 615 07$aFunctions of a complex variable 686 $a30-xx$2msc 701 $aPapadopoulos$b Athanase$059547 801 0$bch0018173 906 $aBOOK 912 $a9910153279403321 996 $aHandbook of Teichmu?ller Theory, Volume VI$92565903 997 $aUNINA