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Journal of Knot Theory and Its Ramifications最新文献

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Strict Inequalities for the n-crossing Number n-交叉数的严格不等式
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-11-26 DOI: 10.1142/s0218216523500281
Nicholas Hagedorn
{"title":"Strict Inequalities for the n-crossing Number","authors":"Nicholas Hagedorn","doi":"10.1142/s0218216523500281","DOIUrl":"https://doi.org/10.1142/s0218216523500281","url":null,"abstract":"In 2013, Adams introduced the $n$-crossing number of a knot $K$, denoted by $c_n(K)$. Inequalities between the $2$-, $3$-, $4$-, and $5$-crossing numbers have been previously established. We prove $c_9(K)leq c_3(K)-2$ for all knots $K$ that are not the trivial, trefoil, or figure-eight knot. We show this inequality is optimal and obtain previously unknown values of $c_9(K)$. We generalize this inequality to prove that $c_{13}(K)<c_{5}(K)$ for a certain set of classes of knots.","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45149761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
The one-row colored 𝔰𝔩3 Jones polynomials for pretzel links 椒盐卷饼链接的单行彩色的<s:1>𝔩3琼斯多项式
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-11-24 DOI: 10.1142/s021821652250105x
Kotaro Kawasoe
{"title":"The one-row colored 𝔰𝔩3 Jones polynomials for pretzel links","authors":"Kotaro Kawasoe","doi":"10.1142/s021821652250105x","DOIUrl":"https://doi.org/10.1142/s021821652250105x","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41510200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Conversion to almost classical virtual links and pseudo Goeritz matrices 转换到几乎经典的虚链接和伪格里茨矩阵
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-11-16 DOI: 10.1142/s0218216522500985
Naoko Kamada
{"title":"Conversion to almost classical virtual links and pseudo Goeritz matrices","authors":"Naoko Kamada","doi":"10.1142/s0218216522500985","DOIUrl":"https://doi.org/10.1142/s0218216522500985","url":null,"abstract":"The notion of a virtual link is a generalization of a classical link. Alexander numbering is a numbering of [Formula: see text] to arcs of a classical link diagram which is due to a numbering to disks of a complement of a link diagram in [Formula: see text]. Every classical link diagram admits Alexander numbering. A virtual link diagram corresponds to a link diagram in a closed oriented surface. Some virtual link diagrams do not admit any Alexander numbering. If a virtual link diagram admits Alexander numbering, we call it an almost classical virtual link diagram. In this paper, we construct a map from the set of virtual link diagrams to that of almost classical virtual link diagrams. It induces a map from the set of virtual links to that of almost classical virtual links. Using this map, we define a kind of Goeritz matrix of virtual link diagrams and introduce invariants of virtual links.","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45527011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Families of Curly Knots 卷曲结族
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-11-14 DOI: 10.1142/s0218216522501012
C. Ernst, S. Harrison
{"title":"Families of Curly Knots","authors":"C. Ernst, S. Harrison","doi":"10.1142/s0218216522501012","DOIUrl":"https://doi.org/10.1142/s0218216522501012","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43599598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On the axioms of singquandles 关于单量子公理
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-11-10 DOI: 10.1142/s0218216522500948
M. Bonatto, A. Cattabriga
{"title":"On the axioms of singquandles","authors":"M. Bonatto, A. Cattabriga","doi":"10.1142/s0218216522500948","DOIUrl":"https://doi.org/10.1142/s0218216522500948","url":null,"abstract":"In this paper, we deal with the notion of singquandles introduced in [I. R. U. Churchill, M. Elhamdadi, M. Hajij and S. Nelson, Singular knots and involutive quandles, J. Knot Theory Ramifications 26(14) (2017) 1750099]. This is an algebraic structure that naturally axiomatizes Reidemeister moves for singular links, similarly to what happens for ordinary links and quandles. We present a new axiomatization that shows different algebraic aspects and simplifies applications. We also reformulate and simplify the axioms for affine singquandles (in particular in the idempotent case).","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47128203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Some congruence of the generalized Alexander invariant for periodic virtual links 周期虚连杆广义亚历山大不变量的若干同余性
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-11-10 DOI: 10.1142/s0218216522500997
Joonoh Kim, Kyoung-Tark Kim
{"title":"Some congruence of the generalized Alexander invariant for periodic virtual links","authors":"Joonoh Kim, Kyoung-Tark Kim","doi":"10.1142/s0218216522500997","DOIUrl":"https://doi.org/10.1142/s0218216522500997","url":null,"abstract":"In this paper, we provide two new congruences of the generalized Alexander polynomial [Formula: see text] for periodic virtual links [Formula: see text]. We use the Yang–Baxter state model of [Formula: see text] introduced by Kauffman and Radford.","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41631515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
The H(n)-move is an unknotting operation for virtual and welded links H(n)移动是虚拟和焊接链路的解结操作
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-11-01 DOI: 10.1142/s021821652350061x
Danish Ali, Zhiqing Yang, Abid Hussain, Mohd Ibrahim Sheikh
{"title":"The H(n)-move is an unknotting operation for virtual and welded links","authors":"Danish Ali, Zhiqing Yang, Abid Hussain, Mohd Ibrahim Sheikh","doi":"10.1142/s021821652350061x","DOIUrl":"https://doi.org/10.1142/s021821652350061x","url":null,"abstract":"An unknotting operation is a local move such that any knot diagram can be transformed into a diagram of the trivial knot by a finite sequence of these operations plus some Reidemeister moves. It is known that the H(n)-move is an unknotting operation for classical knots and links. In this paper, we extend the classical unknotting operation H(n)-move to virtual knots and links. Virtualization and forbidden move are well-known unknotting operations for virtual knots and links. We also show that virtualization and forbidden move can be realized by a finite sequence of generalized Reidemeister moves and H(n)-moves.","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44768950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Structures of homomorphisms induced by arc selection game and arc freeze selection game 弧选择对策和弧冻结选择对策诱导的同态结构
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-10-28 DOI: 10.1142/s0218216522501000
Rin Kinuno
{"title":"Structures of homomorphisms induced by arc selection game and arc freeze selection game","authors":"Rin Kinuno","doi":"10.1142/s0218216522501000","DOIUrl":"https://doi.org/10.1142/s0218216522501000","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44026347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Distinguishing Some Genus One Knots Using Finite Quotients 用有限商判别某些属一结
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-10-28 DOI: 10.1142/s0218216523500359
Tamunonye Cheetham-West
{"title":"Distinguishing Some Genus One Knots Using Finite Quotients","authors":"Tamunonye Cheetham-West","doi":"10.1142/s0218216523500359","DOIUrl":"https://doi.org/10.1142/s0218216523500359","url":null,"abstract":"We give a criterion for distinguishing a prime knot $K$ in $S^3$ from every other knot in $S^3$ using the finite quotients of $pi_1(S^3setminus K)$. Using recent work of Baldwin-Sivek, we apply this criterion to the hyperbolic knots $5_2$, $15n_{43522}$, and the three-strand pretzel knots $P(-3,3,2n+1)$ for every integer $n$.","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41941716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On Torsion in Linearized Legendrian Contact Homology 线性化Legendrian接触同调中的扭转
IF 0.5 4区 数学
Journal of Knot Theory and Its Ramifications Pub Date : 2022-10-17 DOI: 10.1142/S0218216523500566
R. Golovko
{"title":"On Torsion in Linearized Legendrian Contact Homology","authors":"R. Golovko","doi":"10.1142/S0218216523500566","DOIUrl":"https://doi.org/10.1142/S0218216523500566","url":null,"abstract":"In this short note we discuss certain examples of Legendrian submanifolds, whose linearized Legendrian contact (co)homology groups over integers have non-vanishing algebraic torsion. More precisely, for a given arbitrary finitely generated abelian group $G$ and a positive integer $ngeq 3$, $nneq 4$, we construct examples of Legendrian submanifolds of the standard contact vector space $mathbb R^{2n+1}$, whose $n-1$-th linearized Legendrian contact (co)homology over $mathbb Z$ computed with respect to a certain augmentation is isomorphic to $G$.","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46266134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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