Inter-universal geometry と ABC予想 (応援スレ) 44

[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 44 (1002ﾚｽ)
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93: 現代数学の系譜 雑談 ◆e.a0E5TtKE  [] 2020/04/16(木) 23:58:01 ID:2hTnrFrU

>>92
つづき

https://en.wikipedia.org/wiki/William_Thurston
William Thurston
(抜粋)
To complete the picture, Thurston proved a hyperbolization theorem for Haken manifolds. A particularly important corollary is that many knots and links are in fact hyperbolic. Together with his hyperbolic Dehn surgery theorem, this showed that closed hyperbolic 3-manifolds existed in great abundance.

The geometrization theorem has been called Thurston's Monster Theorem, due to the length and difficulty of the proof. Complete proofs were not written up until almost 20 years later. The proof involves a number of deep and original insights which have linked many apparently disparate fields to 3-manifolds.

http://www.mathematik.uni-r.de/friedl/papers/dmv_091514.pdf
THURSTON’S VISION AND THE VIRTUAL FIBERING
THEOREM FOR 3-MANIFOLDS
STEFAN FRIEDL
(抜粋)
Abstract. 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 Perelman’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.

つづく

http://rio2016.5ch.net/test/read.cgi/math/1586655469/93

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