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Arbitrarily large torsion in Khovanov cohomology Khovanov上同调中的任意大扭转
IF 1.1 2区 数学
Quantum Topology Pub Date : 2019-09-16 DOI: 10.4171/QT/149
Sujoy Mukherjee, D. Schuetz
{"title":"Arbitrarily large torsion in Khovanov cohomology","authors":"Sujoy Mukherjee, D. Schuetz","doi":"10.4171/QT/149","DOIUrl":"https://doi.org/10.4171/QT/149","url":null,"abstract":"For any positive integer $k$ and $pin {3,5,7}$ we construct a link which has a direct summand $mathbb{Z}/p^kmathbb{Z}$ in its Khovanov cohomology.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"67 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89800452","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: 4
The Roger–Yang skein algebra and the decorated Teichmüller space 罗杰-杨交织代数和装饰的teichm<e:1>勒空间
IF 1.1 2区 数学
Quantum Topology Pub Date : 2019-09-06 DOI: 10.4171/QT/150
Han-Bom Moon, H. Wong
{"title":"The Roger–Yang skein algebra and the decorated Teichmüller space","authors":"Han-Bom Moon, H. Wong","doi":"10.4171/QT/150","DOIUrl":"https://doi.org/10.4171/QT/150","url":null,"abstract":"Based on hyperbolic geometric considerations, Roger and Yang introduced an extension of the Kauffman bracket skein algebra that includes arcs. In particular, their skein algebra is a deformation quantization of a certain commutative curve algebra, and there is a Poisson algebra homomorphism between the curve algebra and the algebra of smooth functions on decorated Teichmuller space. In this paper, we consider surfaces with punctures which is not the 3-holed sphere and which have an ideal triangulation without self-folded edges or triangles. For those surfaces, we prove that Roger and Yang's Poisson algebra homomorphism is injective, and the skein algebra they defined have no zero divisors. A section about generalized corner coordinates for normal arcs may be of independent interest.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"80 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74170143","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: 6
Four dimensional topological quantum field theories from $G$-crossed braided categories 从$G$交叉编织范畴出发的四维拓扑量子场论
IF 1.1 2区 数学
Quantum Topology Pub Date : 2019-09-06 DOI: 10.4171/qt/128
Shawn X. Cui
{"title":"Four dimensional topological quantum field theories from $G$-crossed braided categories","authors":"Shawn X. Cui","doi":"10.4171/qt/128","DOIUrl":"https://doi.org/10.4171/qt/128","url":null,"abstract":"","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"52 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89919539","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: 21
HOMFLYPT homology for links in handlebodies via type A Soergel bimodules 通过A型Soergel双模的柄体连杆的HOMFLYPT同源性
IF 1.1 2区 数学
Quantum Topology Pub Date : 2019-08-19 DOI: 10.4171/QT/152
David E. V. Rose, D. Tubbenhauer
{"title":"HOMFLYPT homology for links in handlebodies via type A Soergel bimodules","authors":"David E. V. Rose, D. Tubbenhauer","doi":"10.4171/QT/152","DOIUrl":"https://doi.org/10.4171/QT/152","url":null,"abstract":"We define a triply-graded invariant of links in a genus g handlebody, generalizing the colored HOMFLYPT (co)homology of links in the 3-ball. Our main tools are the description of these links in terms of a subgroup of the classical braid group, and a family of categorical actions built from complexes of (singular) Soergel bimodules.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"34 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75305671","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: 9
Embedding Deligne's category $mathrm{Underline{Re}p}(S_t)$ in the Heisenberg category 在Heisenberg范畴中嵌入Deligne的范畴$ mathm {Underline{Re}p}(S_t)$
IF 1.1 2区 数学
Quantum Topology Pub Date : 2019-05-14 DOI: 10.4171/QT/147
Samuel Nyobe Likeng, Alistair Savage
{"title":"Embedding Deligne's category $mathrm{Underline{Re}p}(S_t)$ in the Heisenberg category","authors":"Samuel Nyobe Likeng, Alistair Savage","doi":"10.4171/QT/147","DOIUrl":"https://doi.org/10.4171/QT/147","url":null,"abstract":"We define a faithful linear monoidal functor from the partition category, and hence from Deligne’s category Rep(St), to the additive Karoubi envelope of the Heisenberg category. We show that the induced map on Grothendieck rings is injective and corresponds to the Kronecker coproduct on symmetric functions.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"109 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80843270","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 two-variable series for knot complements 结补的双变量级数
IF 1.1 2区 数学
Quantum Topology Pub Date : 2019-04-12 DOI: 10.4171/QT/145
S. Gukov, Ciprian Manolescu
{"title":"A two-variable series for knot complements","authors":"S. Gukov, Ciprian Manolescu","doi":"10.4171/QT/145","DOIUrl":"https://doi.org/10.4171/QT/145","url":null,"abstract":"The physical 3d $mathcal{N}=2$ theory T[Y] was previously used to predict the existence of some 3-manifold invariants $hat{Z}_{a}(q)$ that take the form of power series with integer coefficients, converging in the unit disk. Their radial limits at the roots of unity should recover the Witten-Reshetikhin-Turaev invariants. In this paper we discuss how, for complements of knots in $S^3$, the analogue of the invariants $hat{Z}_{a}(q)$ should be a two-variable series $F_K(x,q)$ obtained by parametric resurgence from the asymptotic expansion of the colored Jones polynomial. The terms in this series should satisfy a recurrence given by the quantum A-polynomial. Furthermore, there is a formula that relates $F_K(x,q)$ to the invariants $hat{Z}_{a}(q)$ for Dehn surgeries on the knot. We provide explicit calculations of $F_K(x,q)$ in the case of knots given by negative definite plumbings with an unframed vertex, such as torus knots. We also find numerically the first terms in the series for the figure-eight knot, up to any desired order, and use this to understand $hat{Z}_a(q)$ for some hyperbolic 3-manifolds.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"82 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79788928","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: 75
A note on the $Theta$-invariant of 3-manifolds 关于3-流形$Theta$不变量的注记
IF 1.1 2区 数学
Quantum Topology Pub Date : 2019-03-11 DOI: 10.4171/QT/146
A. Cattaneo, Tatsuro Shimizu
{"title":"A note on the $Theta$-invariant of 3-manifolds","authors":"A. Cattaneo, Tatsuro Shimizu","doi":"10.4171/QT/146","DOIUrl":"https://doi.org/10.4171/QT/146","url":null,"abstract":"In this note, we revisit the $Theta$-invariant as defined by R. Bott and the first author. The $Theta$-invariant is an invariant of rational homology 3-spheres with acyclic orthogonal local systems, which is a generalization of the 2-loop term of the Chern-Simons perturbation theory. The $Theta$-invariant can be defined when a cohomology group is vanishing. In this note, we give a slightly modified version of the $Theta$-invariant that we can define even if the cohomology group is not vanishing.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"8 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82689333","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: 1
Goldman–Turaev formality implies Kashiwara–Vergne
IF 1.1 2区 数学
Quantum Topology Pub Date : 2018-12-04 DOI: 10.4171/qt/143
A. Alekseev, Nariya Kawazumi, Y. Kuno, Florian Naef
{"title":"Goldman–Turaev formality implies Kashiwara–Vergne","authors":"A. Alekseev, Nariya Kawazumi, Y. Kuno, Florian Naef","doi":"10.4171/qt/143","DOIUrl":"https://doi.org/10.4171/qt/143","url":null,"abstract":"Let $Sigma$ be a compact connected oriented 2-dimensional manifold with non-empty boundary. In our previous work, we have shown that the solution of generalized (higher genus) Kashiwara-Vergne equations for an automorphism $F in {rm Aut}(L)$ of a free Lie algebra implies an isomorphism between the Goldman-Turaev Lie bialgebra $mathfrak{g}(Sigma)$ and its associated graded ${rm gr}, mathfrak{g}(Sigma)$. In this paper, we prove the converse: if $F$ induces an isomorphism $mathfrak{g}(Sigma) cong {rm gr} , mathfrak{g}(Sigma)$, then it satisfies the Kashiwara-Vergne equations up to conjugation. As an application of our results, we compute the degree one non-commutative Poisson cohomology of the Kirillov-Kostant-Souriau double bracket. The main technical tool used in the paper is a novel characterization of conjugacy classes in the free Lie algebra in terms of cyclic words.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"s1-4 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2018-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85974709","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: 5
The Strong Slope Conjecture for twisted generalized Whitehead doubles 扭曲广义Whitehead双重的强斜率猜想
IF 1.1 2区 数学
Quantum Topology Pub Date : 2018-11-28 DOI: 10.4171/qt/242
K. Baker, Kimihiko Motegi, T. Takata
{"title":"The Strong Slope Conjecture for twisted generalized Whitehead doubles","authors":"K. Baker, Kimihiko Motegi, T. Takata","doi":"10.4171/qt/242","DOIUrl":"https://doi.org/10.4171/qt/242","url":null,"abstract":"The Slope Conjecture proposed by Garoufalidis asserts that the degree of the colored Jones polynomial determines a boundary slope, and its refinement, the Strong Slope Conjecture proposed by Kalfagianni and Tran asserts that the linear term in the degree determines the topology of an essential surface that satisfies the Slope Conjecture. Under certain hypotheses, we show that twisted, generalized Whitehead doubles of a knot satisfies the Slope Conjecture and the Strong Slope Conjecture if the original knot does. Additionally, we provide a proof that there are Whitehead doubles which are not adequate.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"8 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2018-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81943006","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: 8
A polynomial action on colored $mathfrak {sl}_2$ link homology 彩色$mathfrak {sl}_2$链同源上的多项式作用
IF 1.1 2区 数学
Quantum Topology Pub Date : 2018-10-31 DOI: 10.4171/QT/122
Matthew Hogancamp
{"title":"A polynomial action on colored $mathfrak {sl}_2$ link homology","authors":"Matthew Hogancamp","doi":"10.4171/QT/122","DOIUrl":"https://doi.org/10.4171/QT/122","url":null,"abstract":"","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"32 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2018-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83760437","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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