A Primer on Mapping Class Groups (PMS-49) / / Benson Farb, Dan Margalit.
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 givi...
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| Superior document: | Title is part of eBook package: De Gruyter Princeton Mathematical Series eBook Package |
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| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2011] ©2012 |
| Year of Publication: | 2011 |
| Edition: | Course Book |
| Language: | English |
| Series: | Princeton Mathematical Series ;
49 |
| Online Access: | |
| Physical Description: | 1 online resource (512 p.) :; 115 line illus. |
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| LEADER | 08492nam a22019695i 4500 | ||
|---|---|---|---|
| 001 | 9781400839049 | ||
| 003 | DE-B1597 | ||
| 005 | 20220131112047.0 | ||
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| 020 | |a 9781400839049 | ||
| 024 | 7 | |a 10.1515/9781400839049 |2 doi | |
| 035 | |a (DE-B1597)453752 | ||
| 035 | |a (OCoLC)979779983 | ||
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| 100 | 1 | |a Farb, Benson, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 2 | |a A Primer on Mapping Class Groups (PMS-49) / |c Benson Farb, Dan Margalit. |
| 250 | |a Course Book | ||
| 264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2011] | |
| 264 | 4 | |c ©2012 | |
| 300 | |a 1 online resource (512 p.) : |b 115 line illus. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 0 | |a Princeton Mathematical Series ; |v 49 | |
| 505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t Acknowledgments -- |t Overview -- |t Part 1. Mapping Class Groups -- |t Chapter One. Curves, Surfaces, and Hyperbolic Geometry -- |t Chapter Two. Mapping Class Group Basics -- |t Chapter Three. Dehn Twists -- |t Chapter Four. Generating The Mapping Class Group -- |t Chapter Five. Presentations And Low-Dimensional Homology -- |t Chapter Six. The Symplectic Representation and the Torelli Group -- |t Chapter Seven. Torsion -- |t Chapter Eight. The Dehn-Nielsen-Baer Theorem -- |t Chapter Nine. Braid Groups -- |t Part 2. Teichmüller Space and Moduli Space -- |t Chapter Ten. Teichmüller Space -- |t Chapter Eleven. Teichmüller Geometry -- |t Chapter Twelve. Moduli Space -- |t Part 3. The Classification and Pseudo-Anosov Theory -- |t Chapter Thirteen. The Nielsen-Thurston Classification -- |t Chapter Fourteen. Pseudo-Anosov Theory -- |t Chapter Fifteen. Thurston'S Proof -- |t Bibliography -- |t Index |
| 506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
| 520 | |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. A Primer on Mapping Class Groups 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 Teichmüller 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. | ||
| 530 | |a Issued also in print. | ||
| 538 | |a Mode of access: Internet via World Wide Web. | ||
| 546 | |a In English. | ||
| 588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) | |
| 650 | 0 | |a Class groups (Mathematics). | |
| 650 | 0 | |a Mappings (Mathematics). | |
| 650 | 7 | |a MATHEMATICS / Geometry / General. |2 bisacsh | |
| 653 | |a 3-manifold theory. | ||
| 653 | |a Alexander method. | ||
| 653 | |a Birman exact sequence. | ||
| 653 | |a BirmanЈilden theorem. | ||
| 653 | |a Dehn twists. | ||
| 653 | |a DehnЌickorish theorem. | ||
| 653 | |a DehnЎielsenЂaer theorem. | ||
| 653 | |a Dennis Johnson. | ||
| 653 | |a Euler class. | ||
| 653 | |a FenchelЎielsen coordinates. | ||
| 653 | |a Gervais presentation. | ||
| 653 | |a Grtzsch's problem. | ||
| 653 | |a Johnson homomorphism. | ||
| 653 | |a Markov partitions. | ||
| 653 | |a Meyer signature cocycle. | ||
| 653 | |a Mod(S). | ||
| 653 | |a Nielsen realization theorem. | ||
| 653 | |a NielsenДhurston classification theorem. | ||
| 653 | |a NielsenДhurston classification. | ||
| 653 | |a Riemann surface. | ||
| 653 | |a Teichmller mapping. | ||
| 653 | |a Teichmller metric. | ||
| 653 | |a Teichmller space. | ||
| 653 | |a Thurston compactification. | ||
| 653 | |a Torelli group. | ||
| 653 | |a Wajnryb presentation. | ||
| 653 | |a algebraic integers. | ||
| 653 | |a algebraic intersection number. | ||
| 653 | |a algebraic relations. | ||
| 653 | |a algebraic structure. | ||
| 653 | |a annulus. | ||
| 653 | |a aspherical manifold. | ||
| 653 | |a bigon criterion. | ||
| 653 | |a braid group. | ||
| 653 | |a branched cover. | ||
| 653 | |a capping homomorphism. | ||
| 653 | |a classifying space. | ||
| 653 | |a closed surface. | ||
| 653 | |a collar lemma. | ||
| 653 | |a compactness criterion. | ||
| 653 | |a complex of curves. | ||
| 653 | |a configuration space. | ||
| 653 | |a conjugacy class. | ||
| 653 | |a coordinates principle. | ||
| 653 | |a cutting homomorphism. | ||
| 653 | |a cyclic subgroup. | ||
| 653 | |a diffeomorphism. | ||
| 653 | |a disk. | ||
| 653 | |a existence theorem. | ||
| 653 | |a extended mapping class group. | ||
| 653 | |a finite index. | ||
| 653 | |a finite subgroup. | ||
| 653 | |a finite-order homeomorphism. | ||
| 653 | |a finite-order mapping class. | ||
| 653 | |a first homology group. | ||
| 653 | |a geodesic laminations. | ||
| 653 | |a geometric classification. | ||
| 653 | |a geometric group theory. | ||
| 653 | |a geometric intersection number. | ||
| 653 | |a geometric operation. | ||
| 653 | |a geometry. | ||
| 653 | |a harmonic maps. | ||
| 653 | |a holomorphic quadratic differential. | ||
| 653 | |a homeomorphism. | ||
| 653 | |a homological criterion. | ||
| 653 | |a homotopy. | ||
| 653 | |a hyperbolic geometry. | ||
| 653 | |a hyperbolic plane. | ||
| 653 | |a hyperbolic structure. | ||
| 653 | |a hyperbolic surface. | ||
| 653 | |a inclusion homomorphism. | ||
| 653 | |a infinity. | ||
| 653 | |a intersection number. | ||
| 653 | |a isotopy. | ||
| 653 | |a lantern relation. | ||
| 653 | |a low-dimensional homology. | ||
| 653 | |a mapping class group. | ||
| 653 | |a mapping torus. | ||
| 653 | |a measured foliation space. | ||
| 653 | |a measured foliations. | ||
| 653 | |a metric geometry. | ||
| 653 | |a moduli space. | ||
| 653 | |a orbifold. | ||
| 653 | |a orbit. | ||
| 653 | |a outer automorphism group. | ||
| 653 | |a pseudo-Anosov homeomorphism. | ||
| 653 | |a punctured disk. | ||
| 653 | |a quasi-isometry. | ||
| 653 | |a quasiconformal map. | ||
| 653 | |a second homology group. | ||
| 653 | |a simple closed curve. | ||
| 653 | |a simplicial complex. | ||
| 653 | |a stretch factors. | ||
| 653 | |a surface bundles. | ||
| 653 | |a surface homeomorphism. | ||
| 653 | |a surface. | ||
| 653 | |a symplectic representation. | ||
| 653 | |a topology. | ||
| 653 | |a torsion. | ||
| 653 | |a torus. | ||
| 653 | |a train track. | ||
| 700 | 1 | |a Margalit, Dan, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton Mathematical Series eBook Package |z 9783110501063 |o ZDB-23-PMS |
| 773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton University Press eBook-Package Backlist 2000-2013 |z 9783110442502 |
| 776 | 0 | |c print |z 9780691147949 | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/9781400839049 |
| 856 | 4 | 0 | |u https://www.degruyter.com/isbn/9781400839049 |
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