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Quantum Topology最新文献

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Twisting, mutation and knot Floer homology 扭转，突变和结花同源
IF 1.1 2区 数学
Quantum Topology Pub Date : 2016-08-05 DOI: 10.4171/QT/119
Peter Lambert-Cole
{"title":"Twisting, mutation and knot Floer homology","authors":"Peter Lambert-Cole","doi":"10.4171/QT/119","DOIUrl":"https://doi.org/10.4171/QT/119","url":null,"abstract":"Let $mathcal{L}$ be a knot with a fixed positive crossing and $mathcal{L}_n$ the link obtained by replacing this crossing with $n$ positive twists. We prove that the knot Floer homology $widehat{text{HFK}}(mathcal{L}_n)$ `stabilizes' as $n$ goes to infinity. This categorifies a similar stabilization phenomenon of the Alexander polynomial. As an application, we construct an infinite family of prime, positive mutant knots with isomorphic bigraded knot Floer homology groups. Moreover, given any pair of positive mutants, we describe how to derive a corresponding infinite family positive mutants with isomorphic bigraded $widehat{text{HFK}}$ groups, Seifert genera, and concordance invariant $tau$.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"4 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2016-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84736980","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
Classification of Thurston relation subfactor planar algebras Thurston关系子因子平面代数的分类
IF 1.1 2区 数学
Quantum Topology Pub Date : 2016-06-02 DOI: 10.4171/qt/126
Corey Jones, Zhengwei Liu, Yunxiang Ren
{"title":"Classification of Thurston relation subfactor planar algebras","authors":"Corey Jones, Zhengwei Liu, Yunxiang Ren","doi":"10.4171/qt/126","DOIUrl":"https://doi.org/10.4171/qt/126","url":null,"abstract":"Bisch and Jones suggested the skein theoretic classification of planar algebras and investigated the ones generated by 2-boxes with the second author. In this paper, we consider 3-box generators and classify subfactor planar algebras generated by a non-trivial 3-box satisfying a relation proposed by Thurston. The subfactor planar algebras in the classification are either $E^6$ or the ones from representations of quantum $SU(N)$. We introduce a new method to determine positivity of planar algebras and new techniques to reduce the complexity of computations.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"90 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2016-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86797957","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
Categorification of quantum symmetric pairs I 量子对称对的分类1
IF 1.1 2区 数学
Quantum Topology Pub Date : 2016-05-12 DOI: 10.4171/QT/117
Huanchen Bao, P. Shan, Weiqiang Wang, Ben Webster
{"title":"Categorification of quantum symmetric pairs I","authors":"Huanchen Bao, P. Shan, Weiqiang Wang, Ben Webster","doi":"10.4171/QT/117","DOIUrl":"https://doi.org/10.4171/QT/117","url":null,"abstract":"We categorify a coideal subalgebra of the quantum group of $mathfrak{sl}_{2r+1}$ by introducing a $2$-category a la Khovanov-Lauda-Rouquier, and show that self-dual indecomposable $1$-morphisms categorify the canonical basis of this algebra. This allows us to define a categorical action of this coideal algebra on the categories of modules over cohomology rings of partial flag varieties and on the BGG category $mathcal{O}$ of type B/C.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"27 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2016-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83211314","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: 25
Skein and cluster algebras of marked surfaces 标记曲面的束代数和簇代数
IF 1.1 2区 数学
Quantum Topology Pub Date : 2016-01-01 DOI: 10.4171/QT/79
G. Muller
{"title":"Skein and cluster algebras of marked surfaces","authors":"G. Muller","doi":"10.4171/QT/79","DOIUrl":"https://doi.org/10.4171/QT/79","url":null,"abstract":"","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"76 1","pages":"435-503"},"PeriodicalIF":1.1,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89011928","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: 63
On the asymptotic expansion of the Kashaev invariant of the $5_2$ knot $5_2$结Kashaev不变量的渐近展开式
IF 1.1 2区 数学
Quantum Topology Pub Date : 2016-01-01 DOI: 10.4171/QT/83
T. Ohtsuki
{"title":"On the asymptotic expansion of the Kashaev invariant of the $5_2$ knot","authors":"T. Ohtsuki","doi":"10.4171/QT/83","DOIUrl":"https://doi.org/10.4171/QT/83","url":null,"abstract":"We give a presentation of the asymptotic expansion of the Kashaev invariant of the 52 knot. As the volume conjecture states, the leading term of the expansion presents the hyperbolic volume and the Chern-Simons invariant of the complement of the 52 knot. Further, we obtain a method to compute the full Poincare asymptotics to all orders of the Kashaev invariant of the 52 knot.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"66 1","pages":"669-735"},"PeriodicalIF":1.1,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86420733","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: 42
The symplectic properties of the PGL($n,mathbb C$)-gluing equations PGL($n，mathbb C$)-胶合方程的辛性质
IF 1.1 2区 数学
Quantum Topology Pub Date : 2016-01-01 DOI: 10.4171/QT/80
S. Garoufalidis, C. Zickert
{"title":"The symplectic properties of the PGL($n,mathbb C$)-gluing equations","authors":"S. Garoufalidis, C. Zickert","doi":"10.4171/QT/80","DOIUrl":"https://doi.org/10.4171/QT/80","url":null,"abstract":"","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"13 1","pages":"505-551"},"PeriodicalIF":1.1,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75380976","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: 2
Homological algebra related to surfaces with boundary 与有边界曲面相关的同调代数
IF 1.1 2区 数学
Quantum Topology Pub Date : 2015-08-11 DOI: 10.4171/qt/144
K. Cieliebak, K. Fukaya, J. Latschev
{"title":"Homological algebra related to surfaces with boundary","authors":"K. Cieliebak, K. Fukaya, J. Latschev","doi":"10.4171/qt/144","DOIUrl":"https://doi.org/10.4171/qt/144","url":null,"abstract":"In this article we describe an algebraic framework which can be used in three related but different contexts: string topology, symplectic field theory, and Lagrangian Floer theory of higher genus. It turns out that the relevant algebraic structure for all three contexts is a homotopy version of involutive bi-Lie algebras, which we call IBL$_infty$-algebras.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"2016 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2015-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86437072","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: 36
Representations of the Kauffman bracket skein algebra III: closed surfaces and naturality Kauffman托架串代数的表示III:闭面和自然性
IF 1.1 2区 数学
Quantum Topology Pub Date : 2015-05-06 DOI: 10.4171/QT/125
F. Bonahon, H. Wong
{"title":"Representations of the Kauffman bracket skein algebra III: closed surfaces and naturality","authors":"F. Bonahon, H. Wong","doi":"10.4171/QT/125","DOIUrl":"https://doi.org/10.4171/QT/125","url":null,"abstract":"This is the third article in the series begun with [BonWon3, BonWon4], devoted to finite-dimensional representations of the Kauffman bracket skein algebra of an oriented surface $S$. In [BonWon3] we associated a classical shadow to an irreducible representation $rho$ of the skein algebra, which is a character $r_rho in mathcal R_{mathrm{SL}_2(mathbb C)}(S)$ represented by a group homomorphism $pi_1(S) to mathrm{SL}_2(mathbb C)$. The main result of the current article is that, when the surface $S$ is closed, every character $rin mathcal R_{mathrm{SL}_2(mathbb C)}(S)$ occurs as the classical shadow of an irreducible representation of the Kauffman bracket skein algebra. We also prove that the construction used in our proof is natural, and associates to each group homomorphism $rcolon pi_1(S) to mathrm{SL}_2(mathbb C)$ a representation of the skein algebra $mathcal S^A(S)$ that is uniquely determined up to isomorphism.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"30 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2015-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81681110","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: 20
A graph TQFT for hat Heegaard Floer homology 一个图TQFT为该heegard花同调
IF 1.1 2区 数学
Quantum Topology Pub Date : 2015-03-19 DOI: 10.4171/qt/154
Ian Zemke
{"title":"A graph TQFT for hat Heegaard Floer homology","authors":"Ian Zemke","doi":"10.4171/qt/154","DOIUrl":"https://doi.org/10.4171/qt/154","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":1.1,"publicationDate":"2015-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80287401","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
Volume conjectures for the Reshetikhin–Turaev and the Turaev–Viro invariants Reshetikhin-Turaev和Turaev-Viro不变量的体积猜想
IF 1.1 2区 数学
Quantum Topology Pub Date : 2015-03-09 DOI: 10.4171/QT/111
Qingtao Chen, Tian Yang
{"title":"Volume conjectures for the Reshetikhin–Turaev and the Turaev–Viro invariants","authors":"Qingtao Chen, Tian Yang","doi":"10.4171/QT/111","DOIUrl":"https://doi.org/10.4171/QT/111","url":null,"abstract":"We consider the asymptotics of the Turaev-Viro and the Reshetikhin-Turaev invariants of a hyperbolic $3$-manifold, evaluated at the root of unity $exp({2pisqrt{-1}}/{r})$ instead of the standard $exp({pisqrt{-1}}/{r})$. We present evidence that, as $r$ tends to $infty$, these invariants grow exponentially with growth rates respectively given by the hyperbolic and the complex volume of the manifold. This reveals an asymptotic behavior that is different from that of Witten's Asymptotic Expansion Conjecture, which predicts polynomial growth of these invariants when evaluated at the standard root of unity. This new phenomenon suggests that the Reshetikhin-Turaev invariants may have a geometric interpretation other than the original one via $SU(2)$ Chern-Simons gauge theory.","PeriodicalId":51331,"journal":{"name":"Quantum Topology","volume":"103 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2015-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89281660","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: 55
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