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黎曼曲面和热带曲线的模空间导引(英文版)    作 者：Lizhen Ji,Eduard Looijenga　　 ISBN：978-7-04-047419-0　 出版时间：2017-04-28
    • 1 Mapping class groups and Dehn twists
    • Mapping class groups
    • Dehn twists
    • Fundamental groups and mapping class groups
    • 2 Conformal structures and a rough classification
    • Conformal structures
    • Spherical cases
    • Flat cases
    • Hyperbolic cases
    • 3 Geometry of the upper half plane
    • 4 Hyperbolic surfaces
    • Closed geodesics on a hyperbolic surface
    • Geodesic shear
    • Geodesic representation
    • Disjunction of geodesics
    • Pair of pants
    • Pants decompositions
    • Fenchel-Nielsen coordinates
    • Hyperbolic surfaces with cusps
    • Pants decomposition in the presence of cusps
    • 5 Quadratic differentials
    • Local normal form
    • Structure defined by a holomorphic quadratic differential
    • Quadratic differentials and the Teichm¨uller flow
    • 6 Ribbon graphs and ideal triangulation of Teichm¨uller space
    • Jenkins-Strebel differentials
    • Combinatorial description of a graph
    • Ribbon graphs
    • The dual ribbon graph and the arc complex
    • Metrized ribbon graphs
    • Ideal triangulation of thickened Teichm¨uller space
    • 7 The homotopy type of the moduli spacesMg,n
    • The homotopy type ofMg,1
    • The moduli space of curves as a virtual classifying space
    • 8 A brief review of Dolbault cohomology and Serre duality for Riemann surfaces
    • Dolbault cohomology of a coherent sheaf
    • Riemann-Roch and Serre duality for a Riemann surface
    • 9 Deformation theory of Riemann surfaces
    • Orbifolds
    • Towards the complex tangent bundle of Teichm¨uller space
    • Deformation theory
    • The Kodaira Spencermap
    • TheWeil-Petersson metric
    • The quasi-projective structure on the universal family
    • 10 Harvey bordification and Deligne-Mumford compactification
    • The curve complex
    • Harvey’s bordification
    • Stable pointed curves
    • Deformations of nodes
    • Deformations of nodal curves
    • The Deligne-Mumford compactification
    • The idea behindGeometric Invariant Theory
    • Projectivity of the moduli space of stable pointed curves
    • Getting Harvey’s bordification from the D-M compactification
    • 11 Cohomological properties ofMg,P
    • Harer’s stability theorem
    • Hopf algebra structure on stable cohomology
    • 12 Tautological algebras
    • Duality on orbifolds
    • Review of the Gysinmap
    • The moduli space of stable pointed curves as a category
    • Vector bundles on moduli spaces of curves
    • Weighted graphs
    • The notion of a tautological algebra
    • A theoremof Kontsevich
    • Faber’s conjectures
    • Primitivity of the kappa classes
    • References
Part I Moduli Spaces of Riemann Surfaces
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