{"title":"Link homology theories and ribbon concordances","authors":"Sungkyung Kang","doi":"10.4171/qt/162","DOIUrl":null,"url":null,"abstract":"It was recently proved by several authors that ribbon concordances induce injective maps in knot Floer homology, Khovanov homology, and the Heegaard Floer homology of the branched double cover. We give a simple proof of a similar statement in a more general setting, which includes knot Floer homology, Khovanov-Rozansky homologies, and all conic strong Khovanov-Floer theories. This gives a philosophical answer to the question of which aspects of a link TQFT make it injective under ribbon concordances.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"158 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2019-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Topology","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/qt/162","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: 9
Abstract
It was recently proved by several authors that ribbon concordances induce injective maps in knot Floer homology, Khovanov homology, and the Heegaard Floer homology of the branched double cover. We give a simple proof of a similar statement in a more general setting, which includes knot Floer homology, Khovanov-Rozansky homologies, and all conic strong Khovanov-Floer theories. This gives a philosophical answer to the question of which aspects of a link TQFT make it injective under ribbon concordances.
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.
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