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Thurston's Vision and the Virtual Fibering Theorem for 3-Manifolds

机译:瑟斯顿的愿景和三流形的虚拟光纤定理

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摘要

The vision and results of William Thurston (1946-2012) have shaped the theory of 3-dimensional manifolds for the last four decades. The high point was Perel-man's proof of Thurston's Geometrization Conjecture which reduced 3-manifold topology for the most part to the study of hyperbolic 3-manifolds. In 1982 Thurston gave a list of 24 questions and challenges on hyperbolic 3-manifolds. The most daring one came to be known as the Virtual Fibering Conjecture. We will give some background for the conjecture and we will explain its precise content. We will then report on the recent proof of the conjecture by Ian Agol and Dani Wise.
机译:威廉·瑟斯顿(William Thurston,1946-2012年)的视野和成果塑造了过去四十年中的三维流形理论。最高点是Perelman证明了Thurston的Geometrization猜想,该猜想在研究双曲型3流形时减少了3流形拓扑。 1982年,Thurston给出了关于双曲3流形的24个问题和挑战的列表。最大胆的一项被称为虚拟光纤猜想。我们将为猜想提供一些背景,并解释其确切内容。然后,我们将报告Ian Agol和Dani Wise对此猜想的最新证明。

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