Primer on Mapping Class Groups
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A01=Benson Farb
A01=Dan Margalit
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Author_Benson Farb
Author_Dan Margalit
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Automorphism
Big O notation
Bijection
Braid group
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Closed geodesic
Cohomology
Compact space
Compactification (mathematics)
Conjugacy class
Continuous function
Coordinate system
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Corollary
Coset
Covering space
Curve
Dehn twist
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Diagram (category theory)
Diffeomorphism
Dimension (vector space)
Disjoint union
Disk (mathematics)
Division by zero
Eigenvalues and eigenvectors
Elementary matrix
eq_isMigrated=2
eq_nobargain
Equivalence class
Euler characteristic
Exact sequence
Existential quantification
Finite group
Finitely presented
Foliation
Free group
Fundamental domain
Fundamental group
Geometric group theory
Homeomorphism
Homology (mathematics)
Homomorphism
Homotopy
Hyperbolic geometry
Infimum and supremum
Intersection (set theory)
Intersection number (graph theory)
Jordan curve theorem
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Linear map
Mapping class group
Mathematical induction
Metric space
Moduli space
Orbifold
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Quadratic differential
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Riemannian manifold
Simply connected space
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Subgroup
Subset
Summation
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Topology
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Product details
- ISBN 9780691147949
- Weight: 822g
- Dimensions: 152 x 235mm
- Publication Date: 16 Oct 2011
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
- Language: English
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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.
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.
