07036nam 2201945 a 450 991046138270332120200520144314.01-283-22743-697866132274301-4008-3904-110.1515/9781400839049(CKB)2670000000107394(EBL)744105(OCoLC)745866891(SSID)ssj0000544607(PQKBManifestationID)11386007(PQKBTitleCode)TC0000544607(PQKBWorkID)10535999(PQKB)11480860(MiAaPQ)EBC744105(StDuBDS)EDZ0000406791(WaSeSS)Ind00024927(DE-B1597)453752(OCoLC)979779983(DE-B1597)9781400839049(PPN)199244294sudoc(PPN)187957592(Au-PeEL)EBL744105(CaPaEBR)ebr10492894(CaONFJC)MIL322743(EXLCZ)99267000000010739420110302d2012 uy 0engur|n|---|||||txtccrA primer on mapping class groups[electronic resource] /Benson Farb and Dan MargalitCourse BookPrinceton, N.J. Princeton University Press20121 online resource (489 p.)Princeton mathematical series ;49Description based upon print version of record.0-691-14794-9 Includes bibliographical references and index.pt. 1. Mapping class groups -- pt. 2. Teichmüller space and moduli space -- pt. 3. The classification and pseudo-Anosov theory."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 Teichm©oller 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.Princeton mathematical series ;49.Mappings (Mathematics)Class groups (Mathematics)Electronic books.3-manifold theory.Alexander method.Birman exact sequence.BirmanЈilden theorem.Dehn twists.DehnЌickorish theorem.DehnЎielsenЂaer theorem.Dennis Johnson.Euler class.FenchelЎielsen coordinates.Gervais presentation.Grtzsch's problem.Johnson homomorphism.Markov partitions.Meyer signature cocycle.Mod(S).Nielsen realization theorem.NielsenДhurston classification theorem.NielsenДhurston classification.Riemann surface.Teichmller mapping.Teichmller metric.Teichmller space.Thurston compactification.Torelli group.Wajnryb presentation.algebraic integers.algebraic intersection number.algebraic relations.algebraic structure.annulus.aspherical manifold.bigon criterion.braid group.branched cover.capping homomorphism.classifying space.closed surface.collar lemma.compactness criterion.complex of curves.configuration space.conjugacy class.coordinates principle.cutting homomorphism.cyclic subgroup.diffeomorphism.disk.existence theorem.extended mapping class group.finite index.finite subgroup.finite-order homeomorphism.finite-order mapping class.first homology group.geodesic laminations.geometric classification.geometric group theory.geometric intersection number.geometric operation.geometry.harmonic maps.holomorphic quadratic differential.homeomorphism.homological criterion.homotopy.hyperbolic geometry.hyperbolic plane.hyperbolic structure.hyperbolic surface.inclusion homomorphism.infinity.intersection number.isotopy.lantern relation.low-dimensional homology.mapping class group.mapping torus.measured foliation space.measured foliations.metric geometry.moduli space.orbifold.orbit.outer automorphism group.pseudo-Anosov homeomorphism.punctured disk.quasi-isometry.quasiconformal map.second homology group.simple closed curve.simplicial complex.stretch factors.surface bundles.surface homeomorphism.surface.symplectic representation.topology.torsion.torus.train track.Mappings (Mathematics)Class groups (Mathematics)512.7/4SK 260rvkFarb Benson60082Margalit Dan1976-1048740MiAaPQMiAaPQMiAaPQBOOK9910461382703321A primer on mapping class groups2477209UNINA