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Riemann曲面的模空间（影印版）

样章
作者：
Benson Farb，Richard Hain，Eduard Looijenga 编
定价：
169.00元
ISBN：
978-7-04-059309-9
版面字数：
620.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2023-03-23
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
几何学
暂无
  • 前辅文
  • Benson Farb, Richard Hain, and Eduard Looijenga Introduction
  • Yair N. Minsky A Brief Introduction to Mapping Class Groups
    • 1. Definitions, examples, basic structure
    • 2. Hyperbolic geometry, laminations and foliations
    • 3. The Nielsen-Thurston classification theorem
    • 4. Classification continued, and consequences
    • 5. Further reading and current events
    • Bibliography
  • Ursula Hamenst¨adt Teichm¨uller Theory
    • Introduction
    • Lecture 1. Hyperbolic surfaces
    • Lecture 2. Quasiconformal maps
    • Lecture 3. Complex structures, Jacobians and the Weil Petersson form
    • Lecture 4. The curve graph and the augmented Teichm¨uller space
    • Lecture 5. Geometry and dynamics of moduli space
    • Bibliography
  • Nathalie Wahl The Mumford Conjecture, Madsen-Weiss and Homological Stability for Mapping Class Groups of Surfaces
    • Introduction
    • Lecture 1. The Mumford conjecture and the Madsen-Weiss theorem
      • 1. The Mumford conjecture
      • 2. Moduli space, mapping class groups and diffeomorphism groups
      • 3. The Mumford-Morita-Miller classes
      • 4. Homological stability
      • 5. The Madsen-Weiss theorem
      • 6. Exercises
    • Lecture 2. Homological stability: geometric ingredients
      • 1. General strategy of proof
      • 2. The case of the mapping class group of surfaces
      • 3. The ordered arc complex
      • 4. Curve complexes and disc spaces
      • 5. Exercises
    • Lecture 3. Homological stability: the spectral sequence argument
      • 1. Double complexes associated to actions on simplicial complexes
      • 2. The spectral sequence associated to the horizontal filtration
      • 3. The spectral sequence associated to the vertical filtration
      • 4. The proof of stability for surfaces with boundaries
      • 5. Closing the boundaries
      • 6. Exercises
    • Lecture 4. Homological stability: the connectivity argument
      • 1. Strategy for computing the connectivity of the ordered arc complex
      • 2. Contractibility of the full arc complex
      • 3. Deducing connectivity of smaller complexes
      • 4. Exercises
      • Bibliography
  • Soren Galatius Lectures on the Madsen–Weiss Theorem
    • Lecture 1. Spaces of submanifolds and the Madsen–Weiss Theorem
      • 1.1. Spaces of manifolds
      • 1.2. Exercises for Lecture 1
    • Lecture 2. Rational cohomology and outline of proof
      • 2.1. Cohomology of Ω∞Ψ
      • 2.2. Outline of proof
      • 2.3. Exercises for Lecture 2
    • Lecture 3. Topological monoids and the first part of the proof
      • 3.1. Topological monoids
      • 3.2. Exercises for Lecture 3
    • Lecture 4. Final step of the proof
      • 4.1. Proof of theorem 4.3
      • 4.2. Exercises for Lecture 4
    • Bibliography
  • Andrew Putman The Torelli Group and Congruence Subgroups of the Mapping Class Group
    • Introduction
    • Lecture 1. The Torelli group
    • Lecture 2. The Johnson homomorphism
    • Lecture 3. The abelianization of Modg,n(p)
    • Lecture 4. The second rational homology group of Modg(p)
    • Bibliography
  • Carel Faber Tautological Algebras of Moduli Spaces of Curves
    • Introduction
    • Lecture 1. The tautological ring of Mg
      • Exercises
    • Lecture 2. The tautological rings of Mg,n and of some natural partial compactifications of Mg,n
      • Exercises
    • Bibliography
  • Scott A. Wolpert Mirzakhani’s Volume Recursion and Approach for the Witten-Kontsevich Theorem on Moduli Tautological Intersection Numbers
    • Prelude
    • Lecture 1. The background and overview
    • Lecture 2. The McShane-Mirzakhani identity
    • Lecture 3. The covolume formula and recursion
    • Lecture 4. Symplectic reduction, principal S1 bundles and the normal form
    • Lecture 5. The pattern of intersection numbers and Witten-Kontsevich
    • Questions for the problem sessions
    • Bibliography
  • Martin M¨oller Teichm¨uller Curves, Mainly from the Viewpoint of Algebraic Geometry
    • 1. Introduction
    • 2. Flat surfaces and SL2(R)-action
      • 2.1. Flat surfaces and translation structures
      • 2.2. Affine groups and the trace field
      • 2.3. Strata of ΩMg and hyperelliptic loci
      • 2.4. Spin structures and connected components of strata
      • 2.5. Stable differentials and Deligne-Mumford compactification
    • 3. Curves and divisors in Mg
      • 3.1. Curves and fibered surfaces
      • 3.2. Picard groups of moduli spaces
      • 3.3. Special divisors on moduli spaces
      • 3.4. Slopes of divisors and of curves in Mg
    • 4. Variation of Hodge structures and real multiplication
      • 4.1. Hilbert modular varieties and the locus of real multiplication
      • 4.2. Examples
    • 5. Teichm¨uller curves
      • 5.1. Square-tiled surfaces and primitivity
      • 5.2. The VHS of T curves
      • 5.3. Proof of the VHS decomposition and real multiplication
      • 5.4. Cusps and sections of T curves
      • 5.5. The classification problem of T curves: state of the art
    • 6. Lyapunov exponents
      • 6.1. Motivation: Asymptotic cycles, deviations and the wind-tree model
      • 6.2. Lyapunov exponents
      • 6.3. Lyapunov exponents for Teichm¨uller curves
      • 6.4. Non-varying properties for sums of Lyapunov exponents
      • 6.5. Lyapunov exponents for general curves in Mg and in Ag
      • 6.6. Known results and open problems
    • Bibliography
  • Makoto Matsumoto Introduction to arithmetic mapping class groups
    • Introduction
    • Lecture 1. Algebraic fundamental groups
    • Lecture 2. Monodromy representation on fundamental groups
    • Lecture 3. Arithmetic mapping class groups
    • Lecture 4. Topology versus arithmetic
    • Lecture 5. The conjectures of Oda and Deligne-Ihara
    • APPENDIX: Algebraic fundamental groups via fiber functors
    • Bibliography

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