| 词条 | 离散群几何 |
| 释义 | 图书信息书名：离散群几何 出版社: 世界图书出版公司; 第1版 (2011年7月1日) 外文书名: the geometry of discrefe groups 平装: 337页 正文语种: 英语 开本: 24 isbn: 9787510037559 条形码: 9787510037559 商品尺寸: 22.2 x 14.8 x 1.4 cm 商品重量: 481 g 品牌: 世界图书出版公司北京公司 内容简介《离散群几何(英文)》主要内容简介：ThistextisintendedtoserveasanintroductiontothegeometryoftheactionofdiscretegroupsofMobiustransformations.Thesubjectmatterhasnowbeenstudiedwithchangingpointsofemphasisforoverahundredyears,themostrecentdevelopmentsbeingconnectedwiththetheoryof3-manifolds:see,forexample,thepapersofPoincare[77]andThurston[101].About1940,thenowwell-known（butvirtuallyunobtainable）FencheI-Nielsenmanuscriptappeared.Sadly,themanuscriptneverappearedinprint,andthismoremodesttextattemptstodisplayatleastsomeofthebeautifulgeo-metricalideastobefoundinthatmanuscript,aswellassomemorerecentmaterial. 作者简介作者：(英国)比尔登(AlanF.Beardon) 目录CHAPTER 1 Preliminary Material 1.1.Notation 1.2.Inequalities 1.3.Algebra 1.4.Topology 1.5.Topological Groups 1.6.Analysis CHAPTER 2 Matrices 2.1.Non-singular Matrices 2.2.The Metric Structure 2.3.Discrete Groups 2.4.Quaternions 2.5.Unitary Matrices CHAPTER 3 M6bius Transformations on Rn 3.1.The M6bius Group on Rn 3.2.Properties of M6bius Transformations 3.3.The Poincar6 Extension 3.4.Self-mappings of the Unit Ball 3.5.The General Form of a M6bius Transformation 3.6.Distortion Theorems 3.7.The Topological Group Structure 3.8.Notes CHAPTER 4 Complex M6bius Transformations 4.1.Representations by Quaternions 4.2.Representation by Matrices 4.3.Fixed Points and Conjugacy Classes 4.4.Cross Ratios 4.5.The Topology on,M 4.6.Notes CHAPTER 5 Discontinuous Groups 5.1.The Elementary Groups 5.2, Groups with an Invariant Disc 5.3.Discontinuous Groups 5.4.Jrgensen's Inequality 5.5.Notes CHAPTER 6 Riemann Surfaces 6.1.Riemann Surfaces 6.2.Quotient Spaces 6.3.Stable Sets CHAPTER 7 Hyperbolic Geometry Fundamental Concepts 7.1.The Hyperbolic Plane 7.2.The Hyperbolic Metric 7.3.The Geodesics 7.4.The Isometries 7.5.Convex Sets 7.6.Angles Hyperbolic Trigonometry 7.7.Triangles 7.8.Notation 7.9.The Angle of Parallelism 7.10.Triangles with a Vertex at Infinity 7.11.Right-angled Triangles 7.12.The Sine and Cosine Rules 7,13.The Area of a Triangle 7.14.The Inscribed Circle Polygons 7.15.The Area of a Polygon 7.16.Convex Polygons 7,17.Quadrilaterals 7.18.Pentagons 7.19.Hexagons The Geometry of Geodesics 7.20.The Distance of a Point from a Line 7.21.The Perpendicular Bisector of a Segment 7.22.The Common Orthogonal of Disjoint Geodesics 7.23.The Distance Between Disjoint Geodesics 7,24.The Angle Between Intersecting Geodesics 7.25.The Bisector of Two Geodesics 7.26.Transversals Pencils of Geodesics 7.27.The General Theory of Pencils 7.28.Parabolic Pencils 7.29.Elliptic Pencils 7.30.Hyperbolic Pencils The Geometry of lsometries 7.31.The Classification of Isometries 7.32.Parabolic Isometrics 7.33.Elliptic Isometries 7.34.Hyperbolic Isometries 7.35.The Displacement Function 7.36.Isometric Circles 7.37.Canonical Regions 7.38.The Geometry of Products of Isometries 7.39.The Geometry of Commutators 7.40.Notes CHAPTER 8 Fuchsian Groups 8.1.Fuchsian Groups 8.2.Purely Hyperbolic Groups 8.3.Groups Without Elliptic Elements 8.4.Criteria for Discreteness 8.5.The Nielsen Region 8.6.Notes CHAPTER 9 Fundamental Domains 9.1.Fundamental Domains 9.2.Locally Finite Fundamental Domains 9.3.Convex Fundamental Polygons 9.4.The Dirichlet Polygon 9.5.Generalized Dirichlet Polygons 9.6.Fundamental Domains for Coset Decompositions 9.7.Side-Pairing Transformations 9.8.Poincare's Theorem 9.9.Notes CHAPTER 10 Finitely Generated Groups 10.1.Finite Sided Fundamental Polygons 10.2.Points of Approximation 10.3.Conjugacy Classes 10.4.The Signature of a Fuchsian Group 10.5.The Number of Sides of a Fundamental Polygon 10.6.Triangle Groups 10.7.Notes CHAPTER 11 Universal Constraints on Fuchsian Groups i1.1.Uniformity of Discreteness 11.2.Universal Inequalities for Cycles of Vertices 11.3.Hecke Groups 11.4.Trace Inequalities 11.5.Three Elliptic Elements of Order Two 11.6.Universal Bounds on the Displacement Function 11.7.Canonical Regions and Quotient Surfaces 11.8.Notes References Index |
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