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Low-Dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots

Francis Bonahon University of Southern California, Los Angeles, CA
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Softcover ISBN: 978-0-8218-4816-6
Product Code: STML/49
List Price: $55.00 Individual Price:$44.00
Electronic ISBN: 978-1-4704-1634-8
Product Code: STML/49.E
List Price: $54.00 Individual Price:$43.20
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List Price: $82.50 Click above image for expanded view Low-Dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots Francis Bonahon University of Southern California, Los Angeles, CA Available Formats:  Softcover ISBN: 978-0-8218-4816-6 Product Code: STML/49  List Price:$55.00 Individual Price: $44.00  Electronic ISBN: 978-1-4704-1634-8 Product Code: STML/49.E  List Price:$54.00 Individual Price: $43.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$82.50
• Book Details

Student Mathematical Library
IAS/Park City Mathematics Subseries
Volume: 492009; 384 pp
MSC: Primary 51; 30; 57;

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.

This book is published in cooperation with IAS/Park City Mathematics Institute.

Undergraduate students interested in topology and/or geometry of low-dimensional manifolds, particularly 3-manifolds.

• Chapters
• Chapter 1. The euclidean plane
• Chapter 2. The hyperbolic plane
• Chapter 3. The 2-dimensional sphere
• Chapter 4. Gluing constructions
• Chapter 5. Gluing examples
• Chapter 6. Tessellations
• Chapter 7. Group actions and fundamental domains
• Chapter 8. The Farey tessellation and circle packing
• Chapter 9. The 3-dimensional hyperbolic space
• Chapter 10. Kleinian groups
• Chapter 11. The figure-eight knot complement
• Chapter 12. Geometrization theorems in dimension 3
• Appendix. Tool kit

• Reviews

• ...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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
IAS/Park City Mathematics Subseries
Volume: 492009; 384 pp
MSC: Primary 51; 30; 57;

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.

This book is published in cooperation with IAS/Park City Mathematics Institute.

Undergraduate students interested in topology and/or geometry of low-dimensional manifolds, particularly 3-manifolds.

• Chapters
• Chapter 1. The euclidean plane
• Chapter 2. The hyperbolic plane
• Chapter 3. The 2-dimensional sphere
• Chapter 4. Gluing constructions
• Chapter 5. Gluing examples
• Chapter 6. Tessellations
• Chapter 7. Group actions and fundamental domains
• Chapter 8. The Farey tessellation and circle packing
• Chapter 9. The 3-dimensional hyperbolic space
• Chapter 10. Kleinian groups
• Chapter 11. The figure-eight knot complement
• Chapter 12. Geometrization theorems in dimension 3
• Appendix. Tool kit
• ...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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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