Three-Dimensional Geometry and Topology, Vol. 1 by William P. Thurston (PDF)

Description

This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. In the 1920s and 1930s the mathematics of two-dimensional spaces was formalized. It was Thurston’s goal to do the same for three-dimensional spaces. To do this, he had to establish the strong connection of geometry to topology–the study of qualitative questions about geometrical structures. The author created a new set of concepts, and the expression “Thurston-type geometry” has become a commonplace. Three-Dimensional Geometry and Topology had its origins in the form of notes for a graduate course the author taught at Princeton University between 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever requested them. Eventually, the mailing list grew to more than one thousand names. The book is the culmination of two decades of research and has become the most important and influential text in the field. Its content also provided the methods needed to solve one of mathematics’ oldest unsolved problems–the Poincaré Conjecture. In 2005 Thurston won the first AMS Book Prize, for Three-dimensional Geometry and Topology. The prize recognizes an outstanding research book that makes a seminal contribution to the research literature. Thurston received the Fields Medal, the mathematical equivalent of the Nobel Prize, in 1982 for the depth and originality of his contributions to mathematics. In 1979 he was awarded the Alan T. Waterman Award, which recognizes an outstanding young researcher in any field of science or engineering supported by the National Science Foundation.

User’s Reviews

Editorial Reviews: Review “Winner of the 2005 Book Prize, American Mathematical Society””Winner of the 1997 for the Best Professional/Scholarly Book in Mathematics, Association of American Publishers””The present volume represents the culmination of nearly two decades of honoring his famous but difficult 1978 lecture notes. This beautifully produced, exquisitely organized volume now reads as easily as one could possibly hope given the profundity of the material. An instant classic.” ― Choice From the Back Cover This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. About the Author William P. Thurston is the Director of the Mathematical Sciences Research Institute in Berkeley, and Professor of Mathematics at the University of California at Davis. He received the Fields Medal in 1982 for his work on hyperbolic structures on 3-manifolds and foliations. Silvio Levy is editor of Experimental Mathematics and of the MSRI book series. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Thank you.

⭐I am a big fan of Thurston’s work and this book has been very helpful in my exploration of hyperbolic geometry in 3-dimensions.

⭐This book was an instant classic, and for good reason: It conveys many profound insights into geometry and topology discovered by one of the greatest mathematicians of all time — William P. Thurston.If you read this book, know that the more actively you read this, the more you will get out of it. Book is full of exercises for the reader that will greatly enhance your understanding of the material.

⭐Great book. I will be working on some of the problems in it Highly recommend the book. I could give this a 5 star but where is part 2 of the book

⭐Excellent!

⭐I have this book by Jeffery Weeks that Thurston’s opens up with the real mathematics:

⭐. In both cases though, they fail to make the connection of the higher Cartan Lie Algebras to 3 manifold theory clear. When the connection of string theory to 3 dimensional geometry comes through thisapproach to geometry, you think that we have a theory that neglects 5 dimensions and above?So as good as this text is, it still falls somewhat short of what is needed in the modern world and we are forced to think of our own way to interpret the standard model symmetry breaking of SU(5) (Cartan A_4) to U(1)*SU(2)*SU(3).

⭐A must for anyone entering the field of three-dimensional topology and geometry. Most of it is about hyperbolic geometry, which is the biggest area of research in 3-d geometry and topology nowdays.Most of it is readable to undergraduates. Its target audience, though, is beginning graduate students in mathematics. If not already familiar with hyperbolic geometry, you might want to get an introduction to the subject first. Once with this background, though, you will discover there is another level of understanding of hyperbolic space you never realized was possible. One imagines Thurston able to skateboard around hyperbolic space with the kind of geometric understanding he conveys here.What made Thurston so famous and successful as a pioneer in 3-d topology and geometry was his other-worldly geometric intuition. This book takes the reader along the first step of the 10000 miles of getting to that intuition.

⭐FAR worse than Thurston’s classic notes, whence it came. Covers very little material by comparison, and has a lot more bogus “explanations”. Given that the notes are available for free from Math. Sciences Research Inst. (MSRI), in convenient PDF form (for us

⭐and

⭐users, this is not a great book to get.

⭐I wish I could recommend this book more highly, and hesitate to comment at all on a work by such a famous mathematician. However, I have to say that on balance this book disappointed me, though perhaps only because I am ill-equipped to understand it.There are many clear diagrams, and a very helpful glossary at the back. The book is refreshingly free of obscure notation as well. There are many interesting exercises. The text is lively and sometimes amusing.So what is wrong? My first main problem with the book is that the author leaves me behind regularly. His intuition and grasp of the subject make for an over-rapid exposition of difficult ideas. Familiarity with plane Hyperbolic Geometry, or “Cartesian” 3D Euclidean geometry will not help much with this book. Probably readers with a good understanding of Differential Geometry, and a knowledge of Lie Group Theory will get more from this book than I could.My second gripe is that the book resolutely avoids practical computation (for example Moebius transformations are scarcely mentioned). In my view this is a great shame, because on one of the few occasions where the author does descend to a more practical level, there is a very nice derivation of various formulas connected with Spherical and Hyperbolic triangles.I would really have appreciated some solutions to at least some of the exercises.I feel this book should perhaps have had the words Geometry and Topology interchanged in its title. However, there are some very nice Geometric ideas in the book – for example some elegant and non-obvious connections are made between hyperbolic polygons and polyhedra.

⭐Le pavage de S3, l’espace dodécaédral de Poincaré, de Seifert-Weber, les espaces lenticulaires, voilà quelques-unes des merveilles qui attendent le lecteur. Three-Dimensional Geometry and Topology se présente comme un livre d’exemples et W. Thurston fait comprendre son sujet, c’est-à-dire les variétés de dimension 3, en partant d’elles. C’est l’une des originalités de ce livre. La seconde, c’est le recours constant à la signification intuitive et visuelle des résultats. A mon avis, une merveille.

⭐

Keywords

Free Download Three-Dimensional Geometry and Topology, Vol. 1 in PDF format
Three-Dimensional Geometry and Topology, Vol. 1 PDF Free Download
Download Three-Dimensional Geometry and Topology, Vol. 1 1997 PDF Free
Three-Dimensional Geometry and Topology, Vol. 1 1997 PDF Free Download
Download Three-Dimensional Geometry and Topology, Vol. 1 PDF
Free Download Ebook Three-Dimensional Geometry and Topology, Vol. 1