By William P. Thurston
This e-book develops many of the amazing richness, good looks, and tool of geometry in and 3 dimensions, and the robust connection of geometry with topology. Hyperbolic geometry is the celebrity. a powerful attempt has been made to express not only denatured formal reasoning (definitions, theorems, and proofs), yet a dwelling feeling for the topic. there are numerous figures, examples, and routines of various difficulty.
This e-book was once the beginning of a grand scheme constructed by means of Thurston that's now coming to fruition. within the Nineteen Twenties and Nineteen Thirties the math of two-dimensional areas used to be formalized. It used to be Thurston's target to do an analogous for three-d areas. to do that, he needed to identify the robust connection of geometry to topology--the examine of qualitative questions on geometrical buildings. the writer created a brand new set of suggestions, and the expression "Thurston-type geometry" has turn into a commonplace.
Three-Dimensional Geometry and Topology had its origins within the kind of notes for a graduate direction the writer taught at Princeton college among 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever asked them. finally, the mailing record grew to a couple of thousand names. The e-book is the fruits of 2 a long time of study and has develop into crucial and influential textual content within the box. Its content material additionally supplied the equipment had to resolve one in every of arithmetic' oldest unsolved problems--the Poincaré Conjecture.
In 2005 Thurston received the 1st AMS ebook Prize, for Three-dimensional Geometry and Topology. The prize acknowledges a great study e-book that makes a seminal contribution to the examine literature. Thurston bought the Fields Medal, the mathematical similar of the Nobel Prize, in 1982 for the intensity and originality of his contributions to arithmetic. In 1979 he used to be offered the Alan T. Waterman Award, which acknowledges a very good younger researcher in any box of technological know-how or engineering supported by means of the nationwide technological know-how Foundation.