Low-Dimensional Geometry pdf epub mobi txt 電子書 下載2025
- 數學
- 幾何拓撲
- 美國
- 科普
- 教材
- 【科普雜文】
- Spy
- Mathematics
- 低維幾何
- 幾何學
- 拓撲學
- 流形
- 微分幾何
- 歐幾裏得幾何
- 非歐幾何
- 幾何變換
- 空間結構
- 維度分析
具體描述
The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments.
Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory of kleinian groups, and it eventually leads to a discussion of the geometrization theorems for knot complements and 3-dimensional manifolds.
This book is illustrated with many pictures, as the author intended to share his own enthusiasm for the beauty of some of the mathematical objects involved. However, it also emphasizes mathematical rigor and, with the exception of the most recent research breakthroughs, its constructions and statements are carefully justified.
著者簡介
Francis Bonahon: University of Southern California, Los Angeles, CA
圖書目錄
Title page 5
Table of contents 9
Subseries preface 13
Preface 15
The euclidean plane 19
The hyperbolic plane 29
The 2-dimensional sphere 65
Gluing constructions 73
Gluing examples 107
Tessellations 151
Group actions and fundamental domains 203
The Farey tessellation and circle packing 225
The 3-dimensional hyperbolic space 245
Kleinian groups 259
The figure-eight knot complement 311
Geometrization theorems in dimension 3 333
Tool kit 373
Bibliography and references 383
Index 395
Back Cover 403
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An introduction to geometric topology. Plain words with sufficient figures.// 'The remote control' is the key feature, guiding one skip some long detailed proof of theorems at first reading.// Tessellation and figure-eight knot parts are really interesting.// A subject in math that I can accept, but still found it hard to learn.(orz
评分An introduction to geometric topology. Plain words with sufficient figures.// 'The remote control' is the key feature, guiding one skip some long detailed proof of theorems at first reading.// Tessellation and figure-eight knot parts are really interesting.// A subject in math that I can accept, but still found it hard to learn.(orz
评分An introduction to geometric topology. Plain words with sufficient figures.// 'The remote control' is the key feature, guiding one skip some long detailed proof of theorems at first reading.// Tessellation and figure-eight knot parts are really interesting.// A subject in math that I can accept, but still found it hard to learn.(orz
评分An introduction to geometric topology. Plain words with sufficient figures.// 'The remote control' is the key feature, guiding one skip some long detailed proof of theorems at first reading.// Tessellation and figure-eight knot parts are really interesting.// A subject in math that I can accept, but still found it hard to learn.(orz
评分An introduction to geometric topology. Plain words with sufficient figures.// 'The remote control' is the key feature, guiding one skip some long detailed proof of theorems at first reading.// Tessellation and figure-eight knot parts are really interesting.// A subject in math that I can accept, but still found it hard to learn.(orz
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