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New Heegaard Floer slice genus and clasp number bounds 新花片属和苞片数界
IF 1.1 2区 数学
Quantum Topology Pub Date : 2026-10-13 DOI: 10.4171/qt/268
András Juhász,Ian Zemke
{"title":"New Heegaard Floer slice genus and clasp number bounds","authors":"András Juhász,Ian Zemke","doi":"10.4171/qt/268","DOIUrl":"https://doi.org/10.4171/qt/268","url":null,"abstract":"We define several concordance invariants using knot Floer homology, which give improvements over known slice genus and clasp number bounds from Heegaard Floer homology. We also prove that the involutive correction terms of Hendricks and Manolescu give both a slice genus and a clasp number bound.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"11 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A filtered mapping cone formula for cables of the knot meridian 结子午线索的过滤映射锥公式
IF 1.1 2区 数学
Quantum Topology Pub Date : 2026-09-18 DOI: 10.4171/qt/267
Hugo Zhou
{"title":"A filtered mapping cone formula for cables of the knot meridian","authors":"Hugo Zhou","doi":"10.4171/qt/267","DOIUrl":"https://doi.org/10.4171/qt/267","url":null,"abstract":"We construct a filtered mapping cone formula that computes the knot Floer complex of the (n,1) -cable of the knot meridian in any rational surgery, generalizing Truong’s result about the (n,1) -cable of the knot meridian in large surgery and Hedden–Levine’s filtered mapping cone formula. As an application, we show that there exist knots in integer homology spheres with arbitrary varphi_{i,j} values for any i>jgeq 0 , where varphi_{i,j} are the concordance homomorphisms defined in the work of Dai–Hom–Stoffregen–Truong. This formula also leads to the construction of knots in integer homology spheres that bound PL surfaces with arbitrarily large genus in a homology ball in the work of Hom–Stoffregen–Zhou.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"3 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149021044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Odd Khovanov homology and higher representation theory 奇Khovanov同调与高级表征理论
IF 1.1 2区 数学
Quantum Topology Pub Date : 2026-09-11 DOI: 10.4171/qt/266
Léo Schelstraete,Pedro Vaz
{"title":"Odd Khovanov homology and higher representation theory","authors":"Léo Schelstraete,Pedro Vaz","doi":"10.4171/qt/266","DOIUrl":"https://doi.org/10.4171/qt/266","url":null,"abstract":"We introduce a super analogue of mathfrak{gl}_{2} -foams and use it to define an invariant of oriented tangles, shown to coincide with odd Khovanov homology when restricted to links. We then define a supercategorification of the q -Schur algebra of level 2 and realize our construction as a certain super-2-representation. This gives a representation-theoretic construction of odd Khovanov homology, where signs naturally arise as a byproduct of the super-2-categorical structure. In the process, we define a tensor product for chain complexes in super-2-categories, suitably compatible with homotopies. This could be of independent interest.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"7 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148932738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Goldman–Turaev formality from the Kontsevich integral 由Kontsevich积分得到的Goldman-Turaev形式
IF 1.1 2区 数学
Quantum Topology Pub Date : 2026-08-10 DOI: 10.4171/qt/265
Dror Bar-Natan,Zsuzsanna Dancso,Tamara Hogan,Jessica Liu,Nancy Scherich
{"title":"Goldman–Turaev formality from the Kontsevich integral","authors":"Dror Bar-Natan,Zsuzsanna Dancso,Tamara Hogan,Jessica Liu,Nancy Scherich","doi":"10.4171/qt/265","DOIUrl":"https://doi.org/10.4171/qt/265","url":null,"abstract":"We present a new solution to the formality problem for the framed Goldman–Turaev Lie bialgebra in genus zero, constructing Goldman–Turaev homomorphic expansions (formality isomorphisms) from the Kontsevich integral. Our proof uses a three-dimensional derivation of the Goldman–Turaev Lie bialgebra arising from a low-degree Vassiliev quotient – the emergent quotient – of tangles in a thickened punctured disk modulo a Conway skein relation. This is in contrast to Massuyeau’s 2018 proof using braids. A feature of our approach is a general conceptual framework which is applied to prove the compatibility of the homomorphic expansion with both the Goldman bracket and the technically challenging Turaev cobracket.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"8 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Integral Klein bottle surgeries and Heegaard Floer homology 积分克莱因瓶手术和Heegaard flower同源性
IF 1.1 2区 数学
Quantum Topology Pub Date : 2026-07-02 DOI: 10.4171/qt/264
Robert DeYeso III
{"title":"Integral Klein bottle surgeries and Heegaard Floer homology","authors":"Robert DeYeso III","doi":"10.4171/qt/264","DOIUrl":"https://doi.org/10.4171/qt/264","url":null,"abstract":"In this paper, we study which closed, connected, orientable three-manifolds X containing a Klein bottle arise as integral Dehn surgery along a knot in S^{3} . Such X are presentable as a gluing of the twisted I -bundle over the Klein bottle to a knot manifold, and we use a variety of Heegaard Floer-type invariants to generate surgery obstructions. Suppose that X is 8 -surgery along a genus two knot and arises by gluing the twisted I -bundle over the Klein bottle to an S^{3} knot complement. We show that X is an L -space, it must be the dihedral manifold (-1; frac{1}{2}, frac{1}{2}, frac{2}{5}) , and the surgery knot must be K=T(2,5) .","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"6 1","pages":"681-722"},"PeriodicalIF":1.1,"publicationDate":"2026-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148932739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Decategorified Heegaard Floer theory and actions of both $E$ and $F$ 十分类 Heegaard Floer 理论与 $E$ 和 $F$ 的作用
IF 1.1 2区 数学
Quantum Topology Pub Date : 2024-01-08 DOI: 10.4171/qt/204
Andrew Manion
{"title":"Decategorified Heegaard Floer theory and actions of both $E$ and $F$","authors":"Andrew Manion","doi":"10.4171/qt/204","DOIUrl":"https://doi.org/10.4171/qt/204","url":null,"abstract":"","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"4 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139447005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Curves in the disc, the type $B$ braid group, and a type $B$ zigzag algebra 圆盘中的曲线、B$型辫状群和B$型之字形代数
IF 1.1 2区 数学
Quantum Topology Pub Date : 2023-11-22 DOI: 10.4171/qt/198
Edmund Heng, Kie Seng Nge
{"title":"Curves in the disc, the type $B$ braid group, and a type $B$ zigzag algebra","authors":"Edmund Heng, Kie Seng Nge","doi":"10.4171/qt/198","DOIUrl":"https://doi.org/10.4171/qt/198","url":null,"abstract":"","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"725 ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139248767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Invariants of $mathbb{Z}/p$-homology 3-spheres from the abelianization of the level-$p$ mapping class group 从水平-$p$映射类群的无差别化看$mathbb{Z}/p$-homology 3-球体的不变式
IF 1.1 2区 数学
Quantum Topology Pub Date : 2023-11-17 DOI: 10.4171/qt/196
Wolfgang Pitsch, Ricard Riba
{"title":"Invariants of $mathbb{Z}/p$-homology 3-spheres from the abelianization of the level-$p$ mapping class group","authors":"Wolfgang Pitsch, Ricard Riba","doi":"10.4171/qt/196","DOIUrl":"https://doi.org/10.4171/qt/196","url":null,"abstract":"","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"2005 313","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139264357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Evaluating TQFT invariants from $G$-crossed braided spherical fusion categories via Kirby diagrams with 3-handles 用3柄Kirby图求$G$交叉编织球融合范畴的TQFT不变量
2区 数学
Quantum Topology Pub Date : 2023-11-14 DOI: 10.4171/qt/183
Manuel Bärenz
{"title":"Evaluating TQFT invariants from $G$-crossed braided spherical fusion categories via Kirby diagrams with 3-handles","authors":"Manuel Bärenz","doi":"10.4171/qt/183","DOIUrl":"https://doi.org/10.4171/qt/183","url":null,"abstract":"A family of TQFTs parametrised by G-crossed braided spherical fusion categories has been defined recently as a state sum model and as a Hamiltonian lattice model. Concrete calculations of the resulting manifold invariants are scarce because of the combinatorial complexity of triangulations, if nothing else. Handle decompositions, and in particular Kirby diagrams are known to offer an economic and intuitive description of 4-manifolds. We show that if 3-handles are added to the picture, the state sum model can be conveniently redefined by translating Kirby diagrams into the graphical calculus of a G-crossed braided spherical fusion category. ","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"5 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136229844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Actions of $sltwo$ on algebras appearing in categorification $sltwo$对分类中出现的代数的作用
2区 数学
Quantum Topology Pub Date : 2023-11-13 DOI: 10.4171/qt/181
Ben Elias, You Qi
{"title":"Actions of $sltwo$ on algebras appearing in categorification","authors":"Ben Elias, You Qi","doi":"10.4171/qt/181","DOIUrl":"https://doi.org/10.4171/qt/181","url":null,"abstract":"","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"26 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136282070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
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