LEADER 06995nam 2201933 a 450 001 9910789789803321 005 20200520144314.0 010 $a1-283-22743-6 010 $a9786613227430 010 $a1-4008-3904-1 024 7 $a10.1515/9781400839049 035 $a(CKB)2670000000107394 035 $a(EBL)744105 035 $a(OCoLC)745866891 035 $a(SSID)ssj0000544607 035 $a(PQKBManifestationID)11386007 035 $a(PQKBTitleCode)TC0000544607 035 $a(PQKBWorkID)10535999 035 $a(PQKB)11480860 035 $a(StDuBDS)EDZ0000406791 035 $a(WaSeSS)Ind00024927 035 $a(DE-B1597)453752 035 $a(OCoLC)979779983 035 $a(DE-B1597)9781400839049 035 $a(Au-PeEL)EBL744105 035 $a(CaPaEBR)ebr10492894 035 $a(CaONFJC)MIL322743 035 $z(PPN)199244294 035 $a(MiAaPQ)EBC744105 035 $a(PPN)187957592 035 $a(EXLCZ)992670000000107394 100 $a20110302d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 12$aA primer on mapping class groups$b[electronic resource] /$fBenson Farb and Dan Margalit 205 $aCourse Book 210 $aPrinceton, N.J. $cPrinceton University Press$d2012 215 $a1 online resource (489 p.) 225 1 $aPrinceton mathematical series ;$v49 300 $aDescription based upon print version of record. 311 $a0-691-14794-9 320 $aIncludes bibliographical references and index. 327 $apt. 1. Mapping class groups -- pt. 2. Teichmu?ller space and moduli space -- pt. 3. The classification and pseudo-Anosov theory. 330 $a"The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students.The book begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmİoller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification"--Provided by publisher. 410 0$aPrinceton mathematical series ;$v49. 606 $aMappings (Mathematics) 606 $aClass groups (Mathematics) 610 $a3-manifold theory. 610 $aAlexander method. 610 $aBirman exact sequence. 610 $aBirman?ilden theorem. 610 $aDehn twists. 610 $aDehn?ickorish theorem. 610 $aDehn?ielsen?aer theorem. 610 $aDennis Johnson. 610 $aEuler class. 610 $aFenchel?ielsen coordinates. 610 $aGervais presentation. 610 $aGrtzsch's problem. 610 $aJohnson homomorphism. 610 $aMarkov partitions. 610 $aMeyer signature cocycle. 610 $aMod(S). 610 $aNielsen realization theorem. 610 $aNielsen?hurston classification theorem. 610 $aNielsen?hurston classification. 610 $aRiemann surface. 610 $aTeichmller mapping. 610 $aTeichmller metric. 610 $aTeichmller space. 610 $aThurston compactification. 610 $aTorelli group. 610 $aWajnryb presentation. 610 $aalgebraic integers. 610 $aalgebraic intersection number. 610 $aalgebraic relations. 610 $aalgebraic structure. 610 $aannulus. 610 $aaspherical manifold. 610 $abigon criterion. 610 $abraid group. 610 $abranched cover. 610 $acapping homomorphism. 610 $aclassifying space. 610 $aclosed surface. 610 $acollar lemma. 610 $acompactness criterion. 610 $acomplex of curves. 610 $aconfiguration space. 610 $aconjugacy class. 610 $acoordinates principle. 610 $acutting homomorphism. 610 $acyclic subgroup. 610 $adiffeomorphism. 610 $adisk. 610 $aexistence theorem. 610 $aextended mapping class group. 610 $afinite index. 610 $afinite subgroup. 610 $afinite-order homeomorphism. 610 $afinite-order mapping class. 610 $afirst homology group. 610 $ageodesic laminations. 610 $ageometric classification. 610 $ageometric group theory. 610 $ageometric intersection number. 610 $ageometric operation. 610 $ageometry. 610 $aharmonic maps. 610 $aholomorphic quadratic differential. 610 $ahomeomorphism. 610 $ahomological criterion. 610 $ahomotopy. 610 $ahyperbolic geometry. 610 $ahyperbolic plane. 610 $ahyperbolic structure. 610 $ahyperbolic surface. 610 $ainclusion homomorphism. 610 $ainfinity. 610 $aintersection number. 610 $aisotopy. 610 $alantern relation. 610 $alow-dimensional homology. 610 $amapping class group. 610 $amapping torus. 610 $ameasured foliation space. 610 $ameasured foliations. 610 $ametric geometry. 610 $amoduli space. 610 $aorbifold. 610 $aorbit. 610 $aouter automorphism group. 610 $apseudo-Anosov homeomorphism. 610 $apunctured disk. 610 $aquasi-isometry. 610 $aquasiconformal map. 610 $asecond homology group. 610 $asimple closed curve. 610 $asimplicial complex. 610 $astretch factors. 610 $asurface bundles. 610 $asurface homeomorphism. 610 $asurface. 610 $asymplectic representation. 610 $atopology. 610 $atorsion. 610 $atorus. 610 $atrain track. 615 0$aMappings (Mathematics) 615 0$aClass groups (Mathematics) 676 $a512.7/4 686 $aSK 260$2rvk 700 $aFarb$b Benson$060082 701 $aMargalit$b Dan$f1976-$01572609 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910789789803321 996 $aA primer on mapping class groups$93847648 997 $aUNINA