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three-dimensional orbifolds and cone-manifolds, cooper daryl [pdf]

Three dimensional orbifolds and cone-manifolds-World Scientific by Cooper Daryl, Hodgson Craig D. and Kerckhoff Steven P.

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Three dimensional orbifolds and cone-manifolds-World Scientific written by Cooper Daryl, Department of Mathematics, University of California, Santa Barbara, USA and Hodgson Craig D. , Department of Mathematics and Statistics, University of Melbourne, Victoria, Australia and Kerckhoff Steven P. , Stanford University, Stanford USA.

Three dimensional orbifolds and cone-manifolds-World Scientific written by Cooper Daryl, Hodgson Craig D. and Kerckhoff Steven P. cover the following topics.

  • Preface

  • 1. Geometric Structures
    1.1 Geometry of surfaces
    1.2 Geometry of 3-manifolds
    1.3 Thurston’s eight geometries
    1.4 Developing map and holonomy
    1.5 Evidence for the Geometrization Conjecture
    1.6 Geometric structures on 3-manifolds with symmetry
    1.7 Some 3-manifolds with symmetry
    1.8 3-manifolds as branched coverings

  • 2 Orbifolds
    2.1 Orbifold definitions
    2.2 Local structure
    2.3 Orbifold coverings
    2.4 Orbifold Euler characteristic
    2.5 Geometric structures on orbifolds
    2.6 Some geometric 3-orbifolds
    2.7 Orbifold fibrations
    2.8 Orbifold Seifert fibre spaces
    2.9 Suborbifolds
    2.10 Spherical decomposition for orbifolds
    2.11 Euclidean decomposition for orbifolds
    2.12 Graph orbifolds
    2.13 The Orbifold Theorem

  • 3 Cone-Manifolds
    3.1 Definitions
    3.2 Local structure
    3.3 Standard cone neighbourhoods
    3.4 Geodesics
    3.5 Exponential map
    3.6 Dirichlet domains
    3.7 Area and volume of cone-manifolds

  • 4 Two-dimensional Cone-Manifolds
    4.1 Developing map and holonomy
    4.2 Two-dimensional spherical cone-manifolds
    4.3 Two-dimensional euclidean cone-manifolds
    4.4 Euclidean examples with large cone angles
    4.5 Spaces of cone-manifold structures
    4.6 Two-dimensional hyperbolic cone-manifolds

  • 5 Deformations of Hyperbolic Structures
    5.1 Introduction
    5.2 Deformations and degenerations of surfaces
    5.3 General deformation theory
    5.4 Deforming hyperbolic cone-manifolds
    5.5 Representation spaces
    5.6 Hyperbolic Dehn filling
    5.7 Dehn surgery on the figure eight knot

  • 6 Limits of Metrics Spaces
    6.1 ǫ-approximations
    6.2 Limits with basepoints
    6.3 Gromov’s compactness theorem
    6.4 Limits of hyperbolic cone-manifolds
    6.5 Bilipschitz convergence
    6.6 Convergence of holonomy

  • 7 Proof of the Orbifold Theorem
    7.1 Topological preliminaries
    7.2 Deforming hyperbolic structures
    7.3 Controlling degenerations
    7.4 Euclidean to spherical transition
    7.5 Analysis of the thin part
    7.6 Outline of the Collapsing Theorem

  • Background on the Orbifold Theorem

  • References

  • Index

  • Start Now
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