Dehn Fillings of Knot Manifolds Containing Essential Twice-Punctured Tori

IF 4.7 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials Pub Date : 2020-04-08 DOI:10.1090/memo/1469

Steven Boyer, Cameron McA. Gordon, Xingru Zhang

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引用次数: 0

Abstract

We show that if a hyperbolic knot manifold M M contains an essential twice-punctured torus F F with boundary slope β \beta and admits a filling with slope α \alpha producing a Seifert fibred space, then the distance between the slopes α \alpha and β \beta is less than or equal to 5 5 unless M M is the exterior of the figure eight knot. The result is sharp; the bound of 5 5 can be realized on infinitely many hyperbolic knot manifolds. We also determine distance bounds in the case that the fundamental group of the α \alpha -filling contains no non-abelian free group. The proofs are divided into the four cases F F is a semi-fibre, F F is a fibre, F F is non-separating but not a fibre, and F F is separating but not a semi-fibre, and we obtain refined bounds in each case.

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包含基本双穿孔托里的节点漫场的德恩填充

我们证明，如果一个双曲结流形 M M 包含一个边界斜率为 β β 的本质两次穿刺环 F F，并且允许一个斜率为 α α 的填充，从而产生一个塞弗特纤维空间，那么斜率 α α 和 β β 之间的距离小于等于 5 5，除非 M M 是八字结的外部。这个结果是尖锐的；5 5 的边界可以在无限多的双曲结流形上实现。我们还确定了在α α-填充的基群不包含非阿贝尔自由基的情况下的距离界限。证明分为四种情况：F F 是半纤维、F F 是纤维、F F 是非分离的但不是纤维、F F 是分离的但不是半纤维。

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464

期刊介绍： ACS Applied Bio Materials is an interdisciplinary journal publishing original research covering all aspects of biomaterials and biointerfaces including and beyond the traditional biosensing, biomedical and therapeutic applications. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrates knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important bio applications. The journal is specifically interested in work that addresses the relationship between structure and function and assesses the stability and degradation of materials under relevant environmental and biological conditions.