关于 $I\times T^{2}$ 的瞬子与霍瓦诺夫矢量同源性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2020-05-26 DOI:10.4171/qt/184

Yi Xie, Boyu Zhang

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引用次数: 0

摘要

Asaeda、Przytycki 和 Sikora 为紧凑曲面上 $I$ 盆地中的链接定义了 Khovanov 同调的广义。我们证明，对于链接 $Lsubset (-1,1)\times T^2$，当且仅当 $L$ 与嵌入在 $\{0\}\times T^2$ 中的结同构时，$L$ 的 Asaeda-Przytycki-Sikora 同调具有$2$秩和 $\mathbb{Z}/2$ 系数。

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Instantons and Khovanov skein homology on $I\times T^{2}$

Asaeda, Przytycki and Sikora defined a generalization of Khovanov homology for links in $I$-bundles over compact surfaces. We prove that for a link $L\subset (-1,1)\times T^2$, the Asaeda-Przytycki-Sikora homology of $L$ has rank $2$ with $\mathbb{Z}/2$-coefficients if and only if $L$ is isotopic to an embedded knot in $\{0\}\times T^2$.

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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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