The twisted 1-loop invariant and the Jacobian of Ptolemy varieties

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-26 DOI:10.1007/s00209-024-03491-y

Seokbeom Yoon

引用次数: 0

Abstract

We reformulate the twisted 1-loop invariant in terms of Ptolemy coordinates. In addition, we prove that the twisted 1-loop invariant is equal to the adjoint twisted Alexander polynomial for all hyperbolic once-punctured torus bundles. This shows that the 1-loop conjecture proposed by Dimofte and Garoufalidis holds for all hyperbolic once-punctured torus bundles.

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托勒密变体的扭曲一环不变量和雅各布数

我们用托勒密坐标重新表述了扭曲一环不变量。此外，我们还证明了对于所有双曲一次穿孔环束，扭曲一环不变量等于邻接的扭曲亚历山大多项式。这表明迪莫夫特和加鲁法利迪斯提出的单环猜想对所有双曲一次穿孔环束都成立。

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.