Journal of Knot Theory and Its Ramifications最新文献

{"title":"On the 3-loop polynomial of genus 1 knots with trivial Alexander polynomial","authors":"Kouki Yamaguchi","doi":"10.1142/s0218216524500238","DOIUrl":"https://doi.org/10.1142/s0218216524500238","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141807036","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}

{"title":"Quandle coloring quivers of (p,q)-torus links","authors":"Boxin Zhou, Ximin Liu","doi":"10.1142/s0218216524500147","DOIUrl":"https://doi.org/10.1142/s0218216524500147","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141371293","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}

{"title":"A note on Murasugi sum of trivially extendable relative trisections","authors":"Abhijeet Ghanwat, Suhas Pandit, A. Selvakumar","doi":"10.1142/s0218216524500111","DOIUrl":"https://doi.org/10.1142/s0218216524500111","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141387793","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}

{"title":"Some Polynomial Invariants of Virtual Doodles","authors":"Joonoh Kim, Kyoung-Tark Kim","doi":"10.1142/s021821652450010x","DOIUrl":"https://doi.org/10.1142/s021821652450010x","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140992535","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}

{"title":"New Invariants for Virtual Knots via Spanning Surfaces","authors":"Andras Juhasz, Louis H. Kauffman, Eiji Ogasa","doi":"10.1142/s0218216524500093","DOIUrl":"https://doi.org/10.1142/s0218216524500093","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141005591","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}

{"title":"Cyclic coverings of the 3-sphere branched over wild knots of dynamically defined type","authors":"Juan Pablo Díaz, Gabriela Hinojosa","doi":"10.1142/s0218216524500081","DOIUrl":"https://doi.org/10.1142/s0218216524500081","url":null,"abstract":"","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141014930","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}

{"title":"Computation of the knot symmetric quandle and its application to the plat index of surface-links","authors":"Jumpei Yasuda","doi":"10.1142/s0218216524500056","DOIUrl":"https://doi.org/10.1142/s0218216524500056","url":null,"abstract":"<p>A surface-link is a closed surface embedded in the 4-space, possibly disconnected or non-orientable. Every surface-link can be presented by the plat closure of a braided surface, which we call a plat form presentation. The knot symmetric quandle of a surface-link <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>F</mi></math></span><span></span> is a pair of a quandle and a good involution determined from <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>F</mi></math></span><span></span>. In this paper, we compute the knot symmetric quandle for surface-links using a plat form presentation. As an application, we show that for any integers <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>g</mi><mo>≥</mo><mn>0</mn></math></span><span></span> and <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>m</mi><mo>≥</mo><mn>2</mn></math></span><span></span>, there exist infinitely many distinct surface-knots of genus <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>g</mi></math></span><span></span> whose plat indices are <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>m</mi></math></span><span></span>.</p>","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140828851","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}

{"title":"Coefficients of Catalan states of lattice crossing II: Applications of ΘA-state expansions","authors":"Mieczyslaw K. Dabkowski, Cheyu Wu","doi":"10.1142/s0218216524500032","DOIUrl":"https://doi.org/10.1142/s0218216524500032","url":null,"abstract":"<p>Plucking polynomial of a plane rooted tree with a delay function <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>α</mi></math></span><span></span> was introduced in 2014 by Przytycki. As shown in this paper, plucking polynomial factors when <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>α</mi></math></span><span></span> satisfies additional conditions. We use this result and <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi mathvariant=\"normal\">Θ</mi></mrow><mrow><mi>A</mi></mrow></msub></math></span><span></span>-state expansion introduced in our previous work to derive new properties of coefficients <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi><mo stretchy=\"false\">(</mo><mi>A</mi><mo stretchy=\"false\">)</mo></math></span><span></span> of Catalan states <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi></math></span><span></span> resulting from an <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>m</mi><mo stretchy=\"false\">×</mo><mi>n</mi><mo stretchy=\"false\">)</mo></math></span><span></span>-lattice crossing <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mi>L</mi><mo stretchy=\"false\">(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo stretchy=\"false\">)</mo></math></span><span></span>. In particular, we show that <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi><mo stretchy=\"false\">(</mo><mi>A</mi><mo stretchy=\"false\">)</mo></math></span><span></span> factors when <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi></math></span><span></span> has arcs with some special properties. In many instances, this yields a more efficient way for computing <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi><mo stretchy=\"false\">(</mo><mi>A</mi><mo stretchy=\"false\">)</mo></math></span><span></span>. As an application, we give closed-form formulas for coefficients of Catalan states of <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><mi>L</mi><mo stretchy=\"false\">(</mo><mi>m</mi><mo>,</mo><mn>3</mn><mo stretchy=\"false\">)</mo></math></span><span></span>.</p>","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140623948","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}

{"title":"Knot quandle decomposition along a torus","authors":"Marco Bonatto, Alessia Cattabriga, Eva Horvat","doi":"10.1142/s0218216523500980","DOIUrl":"https://doi.org/10.1142/s0218216523500980","url":null,"abstract":"<p>We study the structure of the augmented fundamental quandle of a knot whose complement contains an incompressible torus. We obtain the relationship between the fundamental quandle of a satellite knot and the fundamental quandles/groups of its companion and pattern knots. General presentations of the fundamental quandles of a link in a solid torus, a link in a lens space and a satellite knot are described. In the last part of this paper, an algebraic approach to the study of affine quandles is presented and some known results about the Alexander module and quandle colorings are obtained.</p>","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140199905","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}

{"title":"Heegaard Floer invariants for cyclic 3-orbifolds","authors":"Saibal Ganguli, Mainak Poddar","doi":"10.1142/s0218216523501031","DOIUrl":"https://doi.org/10.1142/s0218216523501031","url":null,"abstract":"<p>We define a notion of Heegaard Floer homology for three-dimensional orbifolds with arbitrary cyclic singularities, generalizing the recent work of Biji Wong where the singular locus is assumed to be connected.</p>","PeriodicalId":54790,"journal":{"name":"Journal of Knot Theory and Its Ramifications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140199908","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}