A graph TQFT for hat Heegaard Floer homology

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2015-03-19 DOI:10.4171/qt/154

Ian Zemke

引用次数: 5

Abstract

In this paper we introduce an extension of the hat Heegaard Floer TQFT which allows cobordisms with disconnected ends. Our construction goes by way of sutured Floer homology, and uses some elementary results from contact geometry. We provide some model computations, which allow us to realize the $H_1(Y;\mathbb{Z})/\text{Tors}$ action and the first order term, $\partial_1$, of the differential of $CF^\infty$ as cobordism maps. As an application we prove a conjectured formula for the action of $\pi_1(Y,p)$ on $\hat{HF}(Y,p)$. We provide enough model computations to completely determine the new cobordism maps without the use of any contact geometric constructions.

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一个图TQFT为该heegard花同调

在本文中，我们介绍了一种扩展的heegard花TQFT，它允许与不连接的端配合。我们的构造采用了Floer同调的方法，并使用了接触几何的一些基本结果。我们提供了一些模型计算，使我们能够将$H_1(Y;\mathbb{Z})/\text{Tors}$的作用和$CF^\infty$的微分的一阶项$\partial_1$实现为协同映射。作为一个应用，我们证明了$\pi_1(Y,p)$对$\hat{HF}(Y,p)$的作用的一个猜想式。我们提供了足够的模型计算来完全确定新的协点映射，而不使用任何接触几何结构。

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.