Thurston’s Broken Windows Only Theorem Revisited

Ken’ichi Ohshika ()
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Ken’ichi Ohshika: Mathematics Department, Gakushuin University

Chapter Chapter 8 in In the Tradition of Thurston III, 2024, pp 275-297 from Springer

Abstract: Abstract The “broken windows only theorem” is the main theorem of the third paper among a series of papers in which Thurston proved his uniformisation theorem for Haken manifolds. In this chapter, we show that the second statement of this theorem is not valid, giving a counter-example. We also give a weaker version of this statement with a proof. In the last section, we speculate on how this second statement was intended to be used in the proof of the bounded image theorem, which constituted a key of the uniformisation theorem. The proof of the bounded image theorem was obtained only quite recently, although a weaker version, which is sufficient for the proof of the uniformisation theorem, had already been proved.

Keywords: Haken manifold uniformisation; Degeneration of hyperbolic structures; Bounded image theorem; 57K32; 30F40 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-43502-7_8

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DOI: 10.1007/978-3-031-43502-7_8

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