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Low-Dimensional Geometry (Student Mathematical Library: IAS/Park City Mathematical Subseries) (Student Mathematical Library: IAS/Park City Mathematical Subseries, 49) - Softcover
Synopsis
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.
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Review
...an essential book, if just because no other yet competes for this crucial niche, but also happily excellent in every respect-passionately told, expertly rendered, exquisitely organized, and sumptuously illustrated. ... Essential. ---- CHOICE Magazine
"About this title" may belong to another edition of this title.
- PublisherAmerican Mathematical Society
- Publication date2009
- ISBN 10 082184816X
- ISBN 13 9780821848166
- BindingPaperback
- LanguageEnglish
- Number of pages391
- Rating
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Low-Dimensional Geometry (Student Mathematical Library: IAS/Park City Mathematical Subseries) (Student Mathematical Library: IAS/Park City Mathematical Subseries, 49)
Published by
American Mathematical Society, 2009
ISBN 10: 082184816X
ISBN 13: 9780821848166
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Low-Dimensional Geometry (Student Mathematical Library: IAS/Park City Mathematical Subseries) (Student Mathematical Library: IAS/Park City Mathematical Subseries, 49)
Published by
American Mathematical Society, 2009
ISBN 10: 082184816X
ISBN 13: 9780821848166
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Low-Dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots (Student Mathematical Library: Mathematical Subseries) (Volume 49)
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American Mathematical Society, 2009
ISBN 10: 082184816X
ISBN 13: 9780821848166
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Low-Dimensional Geometry : From Euclidean Surfaces to Hyperbolic Knots
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American Mathematical Society, 2009
ISBN 10: 082184816X
ISBN 13: 9780821848166
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Low-Dimensional Geometry (Student Mathematical Library: IAS/Park City Mathematical Subseries) (Student Mathematical Library: IAS/Park City Mathematical Subseries, 49)
Published by
American Mathematical Society, 2009
ISBN 10: 082184816X
ISBN 13: 9780821848166
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Low-Dimensional Geometry : From Euclidean Surfaces to Hyperbolic Knots
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American Mathematical Society, 2009
ISBN 10: 082184816X
ISBN 13: 9780821848166
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Lowdimensional Geometry From Euclidean Surfaces to Hyperbolic Knots
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ISBN 13: 9780821848166
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Low-Dimensional Geometry (Student Mathematical Library: IAS/Park City Mathematical Subseries) (Student Mathematical Library: IAS/Park City Mathematical Subseries, 49)
Published by
American Mathematical Society, 2009
ISBN 10: 082184816X
ISBN 13: 9780821848166
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Low-dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots
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American Mathematical Society, 2009
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ISBN 13: 9780821848166
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Low-Dimensional Geometry (Student Mathematical Library: IAS/Park City Mathematical Subseries) (Student Mathematical Library: IAS/Park City Mathematical Subseries, 49)
Published by
American Mathematical Society, 2009
ISBN 10: 082184816X
ISBN 13: 9780821848166
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