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William Paul Thurston (born October 30, 1946) is an American mathematician. He is a pioneer in the field of lowdimensional topology. In 1982, he was awarded the Fields Medal for his contributions to the study of 3manifolds. He is currently a professor of mathematics and computer science at Cornell University (since 2003).
Contents
Mathematical contributions
Foliations
His early work, in the early 1970s, was mainly in foliation theory, where he had a dramatic impact. His more significant results include:
 The proof that every Haefliger structure on a manifold can be integrated to a foliation (this implies, in particular that every manifold with zero Euler characteristic admits a foliation of codimension one).
 The construction of a continuous family of smooth, codimension one foliations on the threesphere whose Godbillon–Vey invariant takes every real value.
In fact, Thurston resolved so many outstanding problems in foliation theory in such a short period of time that, according to Thurston, it led to a kind of exodus from the field, where advisors counselled students against going into foliation theory because Thurston was "cleaning out the subject" (see "On Proof and Progress in Mathematics", especially section 6 ^{[1]}).
The geometrization conjecture
His later work, starting around the late 1970s, revealed that hyperbolic geometry played a far more important role in the general theory of 3manifolds than was previously realised. Prior to Thurston, there were only a handful of known examples of hyperbolic 3manifolds of finite volume, such as the SeifertWeber space. The independent and distinct approaches of Robert Riley and Troels Jørgensen in the midtolate 1970s showed that such examples were less atypical than previously believed; in particular their work showed that the figure eight knot complement was hyperbolic. This was the first example of a hyperbolic knot.
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