The Khovanov homology of infinite braids

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2016-10-14 DOI:10.4171/QT/114

Gabriel Islambouli, Michael Willis

引用次数: 7

Abstract

We show that the limiting Khovanov chain complex of any infinite positive braid categorifies the Jones-Wenzl projector. This result extends Lev Rozansky's categorification of the Jones-Wenzl projectors using the limiting complex of infinite torus braids. We also show a similar result for the limiting Lipshitz-Sarkar-Khovanov homotopy types of the closures of such braids. Extensions to more general infinite braids are also considered.

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无限辫的Khovanov同调

证明了任意无限正辫的极限Khovanov链复合体是Jones-Wenzl投影器的一类。利用无限环面编织的极限复合体，推广了Lev Rozansky关于Jones-Wenzl投影仪的分类。对于此类辫状体闭包的极限Lipshitz-Sarkar-Khovanov同伦类型，我们也给出了类似的结果。扩展到更一般的无限辫子也被考虑。

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.