The Strong Slope Conjecture for twisted generalized Whitehead doubles

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2018-11-28 DOI:10.4171/qt/242

K. Baker, Kimihiko Motegi, T. Takata

引用次数: 8

Abstract

The Slope Conjecture proposed by Garoufalidis asserts that the degree of the colored Jones polynomial determines a boundary slope, and its refinement, the Strong Slope Conjecture proposed by Kalfagianni and Tran asserts that the linear term in the degree determines the topology of an essential surface that satisfies the Slope Conjecture. Under certain hypotheses, we show that twisted, generalized Whitehead doubles of a knot satisfies the Slope Conjecture and the Strong Slope Conjecture if the original knot does. Additionally, we provide a proof that there are Whitehead doubles which are not adequate.

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扭曲广义Whitehead双重的强斜率猜想

Garoufalidis提出的Slope Conjecture认为有色Jones多项式的阶数决定了边界斜率，而Kalfagianni和Tran提出的Strong Slope Conjecture则认为阶数中的线性项决定了满足Slope Conjecture的本质曲面的拓扑结构。在一定的假设下，我们证明了一个结的扭曲的、广义的Whitehead双结点满足斜率猜想，如果原结满足强斜率猜想，则满足强斜率猜想。此外，我们提供了一个证据，证明存在不充分的Whitehead double。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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