一个图TQFT为该heegard花同调

IF 1 2区数学 Q1 MATHEMATICS

Quantum Topology Pub Date : 2015-03-19 DOI:10.4171/qt/154

Ian Zemke

{"title":"一个图TQFT为该heegard花同调","authors":"Ian Zemke","doi":"10.4171/qt/154","DOIUrl":null,"url":null,"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.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"20 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2015-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"A graph TQFT for hat Heegaard Floer homology\",\"authors\":\"Ian Zemke\",\"doi\":\"10.4171/qt/154\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":51331,\"journal\":{\"name\":\"Quantum Topology\",\"volume\":\"20 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2015-03-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum Topology\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/qt/154\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Topology","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/qt/154","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 5

摘要

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。

查看原文本刊更多论文

A graph TQFT for hat Heegaard Floer homology

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Quantum Topology Mathematics-Geometry and Topology

CiteScore

1.80

自引率

9.10%

发文量

期刊介绍： Quantum Topology is a peer reviewed journal dedicated to publishing original research articles, short communications, and surveys in quantum topology and related areas of mathematics. Topics covered include in particular: Low-dimensional Topology Knot Theory Jones Polynomial and Khovanov Homology Topological Quantum Field Theory Quantum Groups and Hopf Algebras Mapping Class Groups and Teichmüller space Categorification Braid Groups and Braided Categories Fusion Categories Subfactors and Planar Algebras Contact and Symplectic Topology Topological Methods in Physics.