Three-Dimensional Geometry and Topology, Volume 1 : : (PMS-35) / / William P. Thurston; ed. by Silvio Levy.
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,...
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Superior document: | Title is part of eBook package: De Gruyter Princeton Mathematical Series eBook Package |
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2014] ©1997 |
Year of Publication: | 2014 |
Language: | English |
Series: | Princeton Mathematical Series ;
1 |
Online Access: | |
Physical Description: | 1 online resource (328 p.) |
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LEADER | 08543nam a22019215i 4500 | ||
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001 | 9781400865321 | ||
003 | DE-B1597 | ||
005 | 20220131112047.0 | ||
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020 | |a 9781400865321 | ||
024 | 7 | |a 10.1515/9781400865321 |2 doi | |
035 | |a (DE-B1597)481419 | ||
035 | |a (OCoLC)984656873 | ||
040 | |a DE-B1597 |b eng |c DE-B1597 |e rda | ||
041 | 0 | |a eng | |
044 | |a nju |c US-NJ | ||
072 | 7 | |a MAT012000 |2 bisacsh | |
082 | 0 | 4 | |a 516/.07 |2 23 |
100 | 1 | |a Thurston, William P., |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 0 | |a Three-Dimensional Geometry and Topology, Volume 1 : |b (PMS-35) / |c William P. Thurston; ed. by Silvio Levy. |
264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2014] | |
264 | 4 | |c ©1997 | |
300 | |a 1 online resource (328 p.) | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a Princeton Mathematical Series ; |v 1 | |
505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t Reader's Advisory -- |t 1 What Is a Manifold? -- |t 2 Hyperbolic Geometry and Its Friends -- |t 3 Geometric Manifolds -- |t 4 The Structure of Discrete Groups -- |t Glossary -- |t Bibliography -- |t Index |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
520 | |a 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. | ||
530 | |a Issued also in print. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) | |
650 | 0 | |a Geometry, Hyperbolic. | |
650 | 0 | |a Three-manifolds (Topology). | |
650 | 7 | |a MATHEMATICS / Geometry / General. |2 bisacsh | |
653 | |a 3-sphere. | ||
653 | |a Abelian group. | ||
653 | |a Affine space. | ||
653 | |a Affine transformation. | ||
653 | |a Atlas (topology). | ||
653 | |a Automorphism. | ||
653 | |a Basis (linear algebra). | ||
653 | |a Bounded set (topological vector space). | ||
653 | |a Brouwer fixed-point theorem. | ||
653 | |a Cartesian coordinate system. | ||
653 | |a Characterization (mathematics). | ||
653 | |a Compactification (mathematics). | ||
653 | |a Conformal map. | ||
653 | |a Contact geometry. | ||
653 | |a Curvature. | ||
653 | |a Cut locus (Riemannian manifold). | ||
653 | |a Diagram (category theory). | ||
653 | |a Diffeomorphism. | ||
653 | |a Differentiable manifold. | ||
653 | |a Dimension (vector space). | ||
653 | |a Dimension. | ||
653 | |a Disk (mathematics). | ||
653 | |a Divisor (algebraic geometry). | ||
653 | |a Dodecahedron. | ||
653 | |a Eigenvalues and eigenvectors. | ||
653 | |a Embedding. | ||
653 | |a Euclidean space. | ||
653 | |a Euler number. | ||
653 | |a Exterior (topology). | ||
653 | |a Facet (geometry). | ||
653 | |a Fiber bundle. | ||
653 | |a Foliation. | ||
653 | |a Fundamental group. | ||
653 | |a Gaussian curvature. | ||
653 | |a Geometry. | ||
653 | |a Group homomorphism. | ||
653 | |a Half-space (geometry). | ||
653 | |a Holonomy. | ||
653 | |a Homeomorphism. | ||
653 | |a Homotopy. | ||
653 | |a Horocycle. | ||
653 | |a Hyperbolic geometry. | ||
653 | |a Hyperbolic manifold. | ||
653 | |a Hyperbolic space. | ||
653 | |a Hyperboloid model. | ||
653 | |a Interior (topology). | ||
653 | |a Intersection (set theory). | ||
653 | |a Isometry group. | ||
653 | |a Isometry. | ||
653 | |a Jordan curve theorem. | ||
653 | |a Lefschetz fixed-point theorem. | ||
653 | |a Lie algebra. | ||
653 | |a Lie group. | ||
653 | |a Line (geometry). | ||
653 | |a Linear map. | ||
653 | |a Linearization. | ||
653 | |a Manifold. | ||
653 | |a Mathematical induction. | ||
653 | |a Metric space. | ||
653 | |a Moduli space. | ||
653 | |a Möbius transformation. | ||
653 | |a Norm (mathematics). | ||
653 | |a Pair of pants (mathematics). | ||
653 | |a Piecewise linear manifold. | ||
653 | |a Piecewise linear. | ||
653 | |a Poincaré disk model. | ||
653 | |a Polyhedron. | ||
653 | |a Projection (linear algebra). | ||
653 | |a Projection (mathematics). | ||
653 | |a Pseudogroup. | ||
653 | |a Pullback (category theory). | ||
653 | |a Quasi-isometry. | ||
653 | |a Quotient space (topology). | ||
653 | |a Riemann mapping theorem. | ||
653 | |a Riemann surface. | ||
653 | |a Riemannian manifold. | ||
653 | |a Sheaf (mathematics). | ||
653 | |a Sign (mathematics). | ||
653 | |a Simplicial complex. | ||
653 | |a Simply connected space. | ||
653 | |a Special linear group. | ||
653 | |a Stokes' theorem. | ||
653 | |a Subgroup. | ||
653 | |a Subset. | ||
653 | |a Tangent space. | ||
653 | |a Tangent vector. | ||
653 | |a Tetrahedron. | ||
653 | |a Theorem. | ||
653 | |a Three-dimensional space (mathematics). | ||
653 | |a Topological group. | ||
653 | |a Topological manifold. | ||
653 | |a Topological space. | ||
653 | |a Topology. | ||
653 | |a Transversal (geometry). | ||
653 | |a Two-dimensional space. | ||
653 | |a Uniformization theorem. | ||
653 | |a Unit sphere. | ||
653 | |a Variable (mathematics). | ||
653 | |a Vector bundle. | ||
653 | |a Vector field. | ||
700 | 1 | |a Levy, Silvio, |e editor. |4 edt |4 http://id.loc.gov/vocabulary/relators/edt | |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton Mathematical Series eBook Package |z 9783110501063 |o ZDB-23-PMS |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton University Press eBook-Package Archive 1927-1999 |z 9783110442496 |
776 | 0 | |c print |z 9780691083049 | |
856 | 4 | 0 | |u https://doi.org/10.1515/9781400865321 |
856 | 4 | 0 | |u https://www.degruyter.com/isbn/9781400865321 |
856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/document/cover/isbn/9781400865321/original |
912 | |a 978-3-11-044249-6 Princeton University Press eBook-Package Archive 1927-1999 |c 1927 |d 1999 | ||
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