Link cobordisms and absolute gradings in link Floer homology

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2017-01-12 DOI:10.4171/QT/124

Ian Zemke

引用次数: 44

Abstract

We show that the link cobordism maps defined by the author are graded and satisfy a grading change formula. Using the grading change formula, we prove a new bound for $\Upsilon_K(t)$ for knot cobordisms in negative definite 4-manifolds. As another application, we show that the link cobordism maps associated to a connected, closed surface in $S^4$ are determined by the genus of the surface. We also prove a new adjunction relation and adjunction inequality for the link cobordism maps. Along the way, we see how many known results in Heegaard Floer homology can be proven using basic properties of the link cobordism maps, together with the grading change formula.

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连杆花同调中的连杆配合和绝对分级

我们证明了作者定义的链接协同映射是分级的，并且满足分级变化公式。利用分级变化公式，证明了负定4流形中结协的一个新的界。作为另一个应用，我们证明了$S^4$中与一个连通的封闭曲面相关联的连杆配合映射是由该曲面的属决定的。我们还证明了连杆协配映射的一个新的附加关系和附加不等式。在此过程中，我们看到有多少已知的Heegaard Floer同调的结果可以用连杆配合映射的基本性质以及分级变化公式来证明。

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.