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Lectures on Hyperbolic Geometry【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

Lectures on Hyperbolic Geometry
  • Riccardo Benedetti，Carlo Pertronio 著
  • 出版社： 北京;西安：世界图书出版公司
  • ISBN：7510046322
  • 出版时间：2012
  • 标注页数：334页
  • 文件大小：68MB
  • 文件页数：349页
  • 主题词：

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图书目录

Chapter A．Hyperbolic Space1

A.1 Models for Hyperbolic Space1

A.2 Isometries of Hyperbolic Space:Hyperboloid Model3

A.3 Conformal Geometry7

A.4 Isometries of Hyperbolic Space:Disc and Half-space Models22

A.5 Geodesics,Hyperbolic Subspaces and Miscellaneous Facts25

A.6 Curvature of Hyperbolic Space37

Chapter B．Hyperbolic Manifolds and the Compact Two-dimensional Case45

B.1 Hyperbolic,Elliptic and Flat Manifolds45

B.2 Topology of Compact Oriented Surfaces55

B.3 Hyperbolic,Elliptic and Flat Surfaces58

B.4 Teiehmüller Space61

Chapter C．The Rigidity Theorem(Compact Case)83

C.1 First Step of the Proof:Extension of Pseudo-isometries84

C.2 Second Step of the Proof:Volume of Ideal Simplices94

C.3 Gromov Norm of a Compact Manifold103

C.4 Third Step of the Proof:the Gromov Norm and the Volume Are Proportional105

C.5 Conclusion of the Proof,Corollaries and Generalizations121

Chapter D．Margulis'Lemma and its Applications133

D.1 Margulis'Lemma133

D.2 Local Geometry of a Hyperbolic Manifold140

D.3 Ends of a Hyperbolic Manifold143

Chapter E．The Space of Hyperbolic Manifolds and the Volume Function159

E.1 The Chabauty and the Geometric Topology160

E.2 Convergence in the Geometric Topology:Opening Cusps The Case of Dimension at least Three174

E.3 The Case of Dimension Different from Three Conclusions and Examples184

E.4 The Three-dimensional Case:Jorgensen's Part of the So-called Jorgensen-Thurston Theory190

E.5 The Three-dimensional Case.Thurston's Hyperbolic Surgery Theorem:Statement and Preliminaries196

E.5-ⅰ Definition and First Properties of T3(Non-compact Three-manifolds with"Triangulation"Without Vertices)198

E.5-ⅱ Hyperbolic Structures on an Element of T3 and Realization of the Complete Structure201

E.5-ⅲ Elements of T3 and Standard Spines207

E.5-ⅳ Some Links Whose Complements are Realized as Elements of T3210

E.6 Proof of Thurston's Hyperbolic Surgery Theorem223

E.6-ⅰ Algebraic Equations of H(M)(Hyperbolic Structures Supported by M∈T3)224

E.6-ⅱ Dimension of H(M):General Case234

E.6-ⅲ The Case M is Complete Hyperbolic:the Space of Deformations251

E.6-ⅳ Completion of the Deformed Hyperbolic Structures and Conclusion of the Proof256

E.7 Applications to the Study of the Volume Function and Complements about Three-dimensional Hyperbolic Geometry267

Chapter F．Bounded Cohomology,a Rough Outline273

F.1 Singular Cohomology273

F.2 Bounded Singular Cohomology277

F.3 Flat Fiber Bundles280

F.4 Euler Class of a Flat Vector Bundle287

F.5 Flat Vector Bundles on Surfaces and the Milnor-Sullivan Theorem294

F.6 Sullivan's Conjecture and Amenable Groups303

Subject Index321

Notation Index324

Referenees326

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