LEADER 07327nam 22016935 450 001 9910163942403321 005 20190708092533.0 010 $a1-4008-6532-8 024 7 $a10.1515/9781400865321 035 $a(CKB)3710000001021047 035 $a(MiAaPQ)EBC4787296 035 $a(DE-B1597)481419 035 $a(OCoLC)984656873 035 $a(DE-B1597)9781400865321 035 $a(EXLCZ)993710000001021047 100 $a20190708d2014 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aThree-Dimensional Geometry and Topology, Volume 1 $eVolume 1 /$fWilliam P. Thurston; Silvio Levy 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2014] 210 4$d©1997 215 $a1 online resource (312 pages) $cillustrations 225 0 $aPrinceton Mathematical Series ;$v1 311 $a0-691-08304-5 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tContents -- $tPreface -- $tReader's Advisory -- $t1 What Is a Manifold? -- $t2 Hyperbolic Geometry and Its Friends -- $t3 Geometric Manifolds -- $t4 The Structure of Discrete Groups -- $tGlossary -- $tBibliography -- $tIndex 330 $aThis 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. 410 0$aPrinceton mathematical series ;$v35. 606 $aGeometry, Hyperbolic 606 $aThree-manifolds (Topology) 610 $a3-sphere. 610 $aAbelian group. 610 $aAffine space. 610 $aAffine transformation. 610 $aAtlas (topology). 610 $aAutomorphism. 610 $aBasis (linear algebra). 610 $aBounded set (topological vector space). 610 $aBrouwer fixed-point theorem. 610 $aCartesian coordinate system. 610 $aCharacterization (mathematics). 610 $aCompactification (mathematics). 610 $aConformal map. 610 $aContact geometry. 610 $aCurvature. 610 $aCut locus (Riemannian manifold). 610 $aDiagram (category theory). 610 $aDiffeomorphism. 610 $aDifferentiable manifold. 610 $aDimension (vector space). 610 $aDimension. 610 $aDisk (mathematics). 610 $aDivisor (algebraic geometry). 610 $aDodecahedron. 610 $aEigenvalues and eigenvectors. 610 $aEmbedding. 610 $aEuclidean space. 610 $aEuler number. 610 $aExterior (topology). 610 $aFacet (geometry). 610 $aFiber bundle. 610 $aFoliation. 610 $aFundamental group. 610 $aGaussian curvature. 610 $aGeometry. 610 $aGroup homomorphism. 610 $aHalf-space (geometry). 610 $aHolonomy. 610 $aHomeomorphism. 610 $aHomotopy. 610 $aHorocycle. 610 $aHyperbolic geometry. 610 $aHyperbolic manifold. 610 $aHyperbolic space. 610 $aHyperboloid model. 610 $aInterior (topology). 610 $aIntersection (set theory). 610 $aIsometry group. 610 $aIsometry. 610 $aJordan curve theorem. 610 $aLefschetz fixed-point theorem. 610 $aLie algebra. 610 $aLie group. 610 $aLine (geometry). 610 $aLinear map. 610 $aLinearization. 610 $aManifold. 610 $aMathematical induction. 610 $aMetric space. 610 $aModuli space. 610 $aMöbius transformation. 610 $aNorm (mathematics). 610 $aPair of pants (mathematics). 610 $aPiecewise linear manifold. 610 $aPiecewise linear. 610 $aPoincaré disk model. 610 $aPolyhedron. 610 $aProjection (linear algebra). 610 $aProjection (mathematics). 610 $aPseudogroup. 610 $aPullback (category theory). 610 $aQuasi-isometry. 610 $aQuotient space (topology). 610 $aRiemann mapping theorem. 610 $aRiemann surface. 610 $aRiemannian manifold. 610 $aSheaf (mathematics). 610 $aSign (mathematics). 610 $aSimplicial complex. 610 $aSimply connected space. 610 $aSpecial linear group. 610 $aStokes' theorem. 610 $aSubgroup. 610 $aSubset. 610 $aTangent space. 610 $aTangent vector. 610 $aTetrahedron. 610 $aTheorem. 610 $aThree-dimensional space (mathematics). 610 $aTopological group. 610 $aTopological manifold. 610 $aTopological space. 610 $aTopology. 610 $aTransversal (geometry). 610 $aTwo-dimensional space. 610 $aUniformization theorem. 610 $aUnit sphere. 610 $aVariable (mathematics). 610 $aVector bundle. 610 $aVector field. 615 0$aGeometry, Hyperbolic. 615 0$aThree-manifolds (Topology) 676 $a516/.07 700 $aThurston$b William P., $061560 702 $aLevy$b Silvio, 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910163942403321 996 $aThree-Dimensional Geometry and Topology, Volume 1$92839652 997 $aUNINA