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Low-Dimensional Geometry (Student Mathematical Library: IAS/Park City Mathematical Subseries) download epub

by Francis Bonahon


Epub Book: 1866 kb. | Fb2 Book: 1662 kb.

Excellent introduction to the subject of low-dimensional geometry

Series: Student Mathematical Library: IAS/Park City Mathematical Subseries (Book 49). Paperback: 391 pages. Excellent introduction to the subject of low-dimensional geometry. I read this book as a warm-up for more advanced topics (algebraic topology, hyperbolic knot theory) and was not disappointed. This book is aimed at advanced undergraduates, but in reality if one has had a good semester of analysis and algebra this book should be very understandable. A passing familiarity with differential geometry will help as well.

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Bonahon F. - Low-Dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots (Student Mathematical Library: Ias Park City Mathematical Subseries). Обсудите книгу на. Нашли опечатку? Выделите ее мышкой и нажмите Ctrl+Enter. 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.

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Low dimensional geometry: from euclidean surfaces to hyperbolic knots. Student Mathematical Library, American Mathematical Society 2009. ISBN 978-0-8218-4816-6. Geodesic laminations on surfaces, in M. Lyubich, John Milnor, Yair Minsky (ed. Laminations and Foliations in Dynamics, Geometry and Topology, Contemporary Mathematics 269, 2001, 1–38. Geometric Structures on 3-manifolds, in R. Daverman, R. Sher (ed. Handbook of Geometric Topology, North Holland 2002, pp. 93–164.

Author: Francis Bonahon. Hyperbolic Geometry (London Mathematical Society Student Texts). Mathematical Epidemiology (Lecture Notes in Mathematics Mathematical Biosciences Subseries). Analytic Hyperbolic Geometry: Mathematical Foundations and Applications. A (Terse) Introduction to Linear Algebra (Student Mathematical Library). A Mathematical Introduction to Wavelets (London Mathematical Society Student Texts).

Student Mathematical Library: IAS/Park City Mathematical Subseries

Student Mathematical Library: IAS/Park City Mathematical Subseries. By (author) Francis Bonahon. "Low-Dimensional Geometry"" starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry.

Student mathematical library IAS/park city mathematical subseries. p. cm. – (Student mathematical library ; v. 49. IAS/Park City mathematical. Volume 49. Low-Dimensional Geometry. From Euclidean Surfaces to Hyperbolic Knots. American Mathematical Society, Providence, Rhode Island Institute for Advanced Study, Princeton, New Jersey. subseries) Includes bibliographical references and index. ISBN 978-0-8218-4816-6 (alk. paper) 1. Manifolds (Mathematics) 2. Geometry, Hyperbolic.

Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. This includes the tessellations associated to the process of gluing together the sides of a polygon.

Low-Dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots (Student Mathematical Library: Ias Park City Mathematical Subseries). Category: M Mathematics, MD Geometry and topology. Category: Математика, Геометрия и топология. 4 Mb. Low-dimensional geometry: From Euclidean surfaces to hyperbolic knots.

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.

Comments: (3)

Blackbeard
Great book! Although, I definitely was not prepared for it! I had to pick up a book on differential geometry (springer undergraduate series has a decent one) and another on introductory hyperbolic geometry (e.g. Greenberg) and THEN I was ready for this one. I'm not entirely too knowledgeable about mathland - I'm in community college and older and more or less going through this stuff on my own for fun (so take my review with many grains of salt) - but I'd say difficulty wise this lands smack-dab in the middle of Mumford, Series, Wright's "Indra's Pearls" and Marden's Outer Circles. It does take a different route than other books (and this is right in the Preface): "We decided to follow a different strategy, by discussing quotient (semi-)metrics very early on and in their full generality. This approach is, in our view, much more intuitive, but it comes with a price: Some proofs become somewhat technical." So yeah, it's great in its approach; it just sure ain't easy. Some of the proofs are over 2 pages long (although the author is very cute - he uses a television remote symbol where the proof starts to signify the start and end of the longer proofs).

On a side note, I'm a bit of a queen when it comes to font, typesetting, illustrations, etc. And so far I've had very good luck with AMS' Student Mathematical Library (of which this is published under). The layout and font and overall quality of the publishing definitely make this much more suitable for studying the material on your own.
DART-SKRIMER
Excellent introduction to the subject of low-dimensional geometry. I read this book as a warm-up for more advanced topics (algebraic topology, hyperbolic knot theory) and was not disappointed. This book is aimed at advanced undergraduates, but in reality if one has had a good semester of analysis and algebra this book should be very understandable. A passing familiarity with differential geometry will help as well.
TheMoonix
This is a good book for a wide range of readers. Aimed at "dedicated" undergraduates, it has valuable lessons for the most advanced of algebraic topologists (Figure 12.5.) as well as, say, a 10 year old beginner (Exercise 12.8.). Those who can't understand the text will enjoy looking at the pictures (e.g., Figure 5.4.).
Low-Dimensional Geometry (Student Mathematical Library: IAS/Park City Mathematical Subseries) download epub
Science & Mathematics
Author: Francis Bonahon
ISBN: 082184816X
Category: Other
Subcategory: Science & Mathematics
Language: English
Publisher: American Mathematical Society; New ed. edition (August 5, 2009)
Pages: 391 pages