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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.
The ending lamination theorem, originally conjectured by William Thurston and later proven by Jeffrey Brock, Richard Canary, and Yair Minsky, states that hyperbolic 3-manifolds with finitely generated fundamental groups are determined by their topology together with certain "end invariants", which are geodesic laminations on some surfaces in ...
In mathematics, Thurston's geometrization conjecture (now a theorem) states that each of certain three-dimensional topological spaces has a unique geometric structure that can be associated with it. It is an analogue of the uniformization theorem for two-dimensional surfaces , which states that every simply connected Riemann surface can be ...
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]
William Thurston. 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.
More precisely, Thurston's hyperbolic Dehn surgery theorem implies that a manifold with cusps is a limit of a sequence of manifolds with cusps for any <, so that the isolated points are volumes of compact manifolds, the manifolds with exactly one cusp are limits of compact manifolds, and so on. Together with results of Jørgensen the theorem ...
In the mathematical subfield of 3-manifolds, the virtually fibered conjecture, formulated by American mathematician William Thurston, states that every closed, irreducible, atoroidal 3-manifold with infinite fundamental group has a finite cover which is a surface bundle over the circle.