Augmented Legendrian cobordism in $J^1S^1$

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-25 DOI:10.4171/qt/195

Yu Pan, Dan Rutherford

引用次数: 0

Abstract

We consider Legendrian links and tangles in $J^1S^1$ and $J^1\[0,1]$ equipped with Morse complex families over a field $\mathbb{F}$ and classify them up to Legendrian cobordism. When the coefficient field is $\mathbb{F}\_2$, this provides a cobordism classification for Legendrians equipped with augmentations of the Legendrian contact homology DG-algebras. A complete set of invariants, for which arbitrary values may be obtained, is provided by the fiber cohomology, a graded monodromy matrix, and a mod $2$ spin number. We apply the classification to construct augmented Legendrian surfaces in $J^1M$ with $\mathrm{dim} M = 2$ realizing any prescribed monodromy representation, $\Phi:\pi\_1(M,x\_0) \to \mathrm{GL}(\mathbf{n}, \mathbb{F})$.

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$J^1S^1$中的增广legendard协同

我们考虑了在场$\mathbb{F}$上具有莫尔斯复族的$J^1S^1$和$J^1\[0,1]$中的勒让连链和缠结，并将它们分类为勒让连协。当系数域为$\mathbb{F}\_2$时，这为配备了Legendrian接触同调dg -代数的增广的Legendrian提供了一种协配分类。由光纤上同调、梯度单矩阵和模$2$自旋数提供了一组可以得到任意值的不变量。我们应用分类构造了$J^1M$中的增广Legendrian曲面，其中$\mathrm{dim} M = 2$实现了任意规定的单形表示，$\Phi:\pi\_1(M,x\_0) \to \mathrm{GL}(\mathbf{n}, \mathbb{F})$。

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.