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Strongly irreducible Heegaard splittings of hyperbolic 3-manifolds
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-06-30 , DOI: 10.1090/proc/15114
Tejas Kalelkar

Abstract:Colding and Gabai have given an effective version of Li's theorem that non-Haken hyperbolic 3-manifolds have finitely many irreducible Heegaard splittings. As a corollary of their work, we show that Haken hyperbolic 3-manifolds have a finite collection of strongly irreducible Heegaard surfaces $ S_i$ and incompressible surfaces $ K_j$ such that any strongly irreducible Heegaard surface is a Haken sum $ S_i + \sum _j n_j K_j$, up to one-sided associates of the Heegaard surfaces.


中文翻译:

双曲3流形的强不可约Heegaard分裂

摘要:Colding和Gabai给出了李定理的有效形式,即非Haken双曲3流形具有有限的许多不可约Heegaard分裂。作为他们工作的推论,我们证明了Haken双曲3流形具有极强不可约Heegaard曲面$ S_i $和不可压缩曲面的有限集合,$ K_j $因此任何极不可约Heegaard曲面都是Haken和,直至Heegaard曲面的单边缔合。 $ S_i + \ sum _j n_j K_j $
更新日期:2020-08-20
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