A Primer on Mapping Class Groups by Benson Farb
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 Teichmuller 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.-
Three-Dimensional Geometry and Topology, Volume 1
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Real Submanifolds in Complex Space and Their Mappings
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The Topology of Fibre Bundles
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Homological Algebra
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The Global Nonlinear Stability of the Minkowski Space
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Pseudodifferential Operators
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Problems in Analysis
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Global Analysis
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Topics in Ergodic Theory
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Hypo-Analytic Structures
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Differential and Combinatorial Topology
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Dimension Theory
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Foundations of Algebraic Analysis
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Convex Analysis
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Mathematical Methods of Statistics
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Topology of 4-Manifolds
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Étale Cohomology
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Lectures on Kahler Groups
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Representation Theory of Semisimple Groups
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Introduction to Fourier Analysis on Euclidean Spaces
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Theory of Lie Groups
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Laplace Transform
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Riemann Surfaces
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Essays on Fourier Analysis in Honor of Elias M. Stein
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Abelian Varieties with Complex Multiplication and Modular Functions
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Spin Geometry
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Singular Integrals and Differentiability Properties of Functions
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Cohomological Induction and Unitary Representations
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Harmonic Analysis
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The Classical Groups
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Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane
"It is clear that a lot of care has been taken in the production of this book, something that indicates the authors' love for the subjectThis book should now become the standard text for the subject."--Stephen P Humphries, Mathematical Reviews "[T]his is a very pleasant and appealing book and it is an excellent reference for any reader willing to learn about this fascinating part of mathematics."--Raquel Diaz, Alvaro Martinez, European Mathematical Society
Benson Farb is professor of mathematics at the University of Chicago. He is the editor of "Problems on Mapping Class Groups and Related Topics" and the coauthor of "Noncommutative Algebra". Dan Margalit is assistant professor of mathematics at Georgia Institute of Technology.
| SKU | Unavailable |
| ISBN 13 | 9780691147949 |
| ISBN 10 | 0691147949 |
| Title | A Primer on Mapping Class Groups |
| Author | Benson Farb |
| Series | Princeton Mathematical Series |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Princeton University Press |
| Year published | 2011-10-16 |
| Number of pages | 488 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |