Link homology theories and ribbon concordances

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2019-09-16 DOI:10.4171/qt/162

Sungkyung Kang

引用次数: 9

Abstract

It was recently proved by several authors that ribbon concordances induce injective maps in knot Floer homology, Khovanov homology, and the Heegaard Floer homology of the branched double cover. We give a simple proof of a similar statement in a more general setting, which includes knot Floer homology, Khovanov-Rozansky homologies, and all conic strong Khovanov-Floer theories. This gives a philosophical answer to the question of which aspects of a link TQFT make it injective under ribbon concordances.

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链接同源理论和条带一致性

近年来，一些作者证明了带状一致性在分枝重盖的结花同源性、Khovanov同源性和Heegaard花同源性中诱导了内射映射。我们在更一般的情况下给出了一个类似命题的简单证明，其中包括结花同调、Khovanov-Rozansky同调和所有的二次强khovanov - flower理论。这给出了一个哲学的答案，一个链接TQFT的哪些方面使它在带一致性下注入的问题。

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.