Трехмерная топология и геометрия. Том 1 1

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.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, Whichrecognizes An Outstanding Young Researcher In Any Field Of Science Or Engineering Supported By The National Science Foundation.

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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.

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 Poincar 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. 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. Every mathematician should be acquainted with the basic facts about the geometry of surfaces, of two-dimensional manifolds. The theory of three-dimensional manifolds is much more difficult and still only partly understood, although there is ample evidence that the theory of three-dimensional manifolds is one of the most beautiful in the whole of mathematics. This excellent introductory work makes this mathematical wonderland remained rather inaccessible to non-specialists. The author is both a leading researcher, with a formidable geometric intuition, and a gifted expositor. His vivid descriptions of what it might be like to live in this or that three-dimensional manifold bring the subject to life. Like Poincaré, he appeals to intuition, but his enthusiasm is infectious and should make many converts for this kind of mathematics. There are good pictures, plenty of exercises and problems, and the reader will find a selection of topics which are not found in the standard repertoire. This book contains a great deal of interesting mathematics Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning, but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book develops some of the power of geometry in two and three dimensions, and the strong connection of geometry with topology.