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The geometry and topology of three-manifolds is a set of widely circulated notes for a graduate course taught at Princeton University by William Thurston from 1978 to 1980 describing his work on 3-manifolds. They were written by Thurston, assisted by students William Floyd and Steven Kerchoff. [1]
William Paul Thurston (October 30, 1946 – August 21, 2012) was an American mathematician.He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds.
A 3-dimensional model geometry X is relevant to the geometrization conjecture if it is maximal and if there is at least one compact manifold with a geometric structure modelled on X. Thurston classified the 8 model geometries satisfying these conditions; they are listed below and are sometimes called Thurston geometries.
American mathematician William Thurston. Thurston's 24 questions are a set of mathematical problems in differential geometry posed by American mathematician William Thurston in his influential 1982 paper Three-dimensional manifolds, Kleinian groups and hyperbolic geometry published in the Bulletin of the American Mathematical Society. [1]
Thurston, William P. (1997), Three-dimensional geometry and topology, Princeton, NJ: Princeton University Press, ISBN 0-691-08304-5, MR 1435975; Adams, Colin Conrad (2004), The Knot Book. An elementary introduction to the mathematical theory of knots.
Gromov's topology utilizes the Gromov-Hausdorff metric and is defined on pointed hyperbolic 3-manifolds. One essentially considers better and better bi-Lipschitz homeomorphisms on larger and larger balls. This results in the same notion of convergence as above as the thick part is always connected; thus, a large ball will eventually encompass ...
His book The Shape of Space: How to Visualize Surfaces and Three-dimensional Manifolds (Marcel Dekker, 1985, ISBN 0-8247-7437-X) explores the geometry and topology of low-dimensional manifolds. [ 3 ] [ 4 ] The second edition (2002, ISBN 0-8247-0709-5 ) explains some of his work in applying the material to cosmology.
The Geometry and Topology of Three-Manifolds, 1980 Princeton lecture notes on geometric structures on 3-manifolds, that states his elliptization conjecture near the beginning of section 3. This Riemannian geometry -related article is a stub .