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Algebraic links in lens spaces 透镜空间中的代数连杆
arXiv: Geometric Topology Pub Date : 2020-02-24 DOI: 10.1142/s0219199720500662
E. Horvat
{"title":"Algebraic links in lens spaces","authors":"E. Horvat","doi":"10.1142/s0219199720500662","DOIUrl":"https://doi.org/10.1142/s0219199720500662","url":null,"abstract":"The lens space $L_{p,q}$ is the orbit space of a $mathbb{Z}_{p}$-action on the three sphere. We investigate polynomials of two complex variables that are invariant under this action, and thus define links in $L_{p,q}$. We study properties of these links, and their relationship with the classical algebraic links. We prove that all algebraic links in lens spaces are fibered, and obtain results about their Seifert genus. We find some examples of algebraic knots in lens spaces, whose lift in the $3$-sphere is a torus link.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85010472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
S-stable foliations on flow-spines with transverse Reeb flow 具有横向Reeb流的流棘上的s稳定叶理
arXiv: Geometric Topology Pub Date : 2020-02-21 DOI: 10.32917/H2020026
Shin Handa, M. Ishikawa
{"title":"S-stable foliations on flow-spines with transverse Reeb\u0000 flow","authors":"Shin Handa, M. Ishikawa","doi":"10.32917/H2020026","DOIUrl":"https://doi.org/10.32917/H2020026","url":null,"abstract":"The notion of S-stability of foliations on branched simple polyhedrons is introduced by R. Benedetti and C. Petronio in the study of characteristic foliations of contact structures on 3-manifolds. We additionally assume that the 1-form $beta$ defining a foliation on a branched simple polyhedron $P$ satisfies $dbeta>0$, which means that the foliation is a characteristic foliation of a contact form whose Reeb flow is transverse to $P$. In this paper, we show that if there exists a 1-form $beta$ on $P$ with $dbeta>0$ then we can find a 1-form with the same property and additionally being S-stable. We then prove that the number of simple tangency points of an S-stable foliation on a positive or negative flow-spine is at least 2 and give a recipe for constructing a characteristic foliation of a 1-form $beta$ with $dbeta>0$ on the abalone.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74835446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Derived Traces of Soergel Categories Soergel范畴的衍生轨迹
arXiv: Geometric Topology Pub Date : 2020-02-14 DOI: 10.1093/IMRN/RNAB019
E. Gorsky, Matthew Hogancamp, Paul Wedrich
{"title":"Derived Traces of Soergel Categories","authors":"E. Gorsky, Matthew Hogancamp, Paul Wedrich","doi":"10.1093/IMRN/RNAB019","DOIUrl":"https://doi.org/10.1093/IMRN/RNAB019","url":null,"abstract":"Author(s): Gorsky, Eugene; Hogancamp, Matthew; Wedrich, Paul | Abstract: We study two kinds of categorical traces of (monoidal) dg categories, with particular interest in categories of Soergel bimodules. First, we explicitly compute the usual Hochschild homology, or derived vertical trace, of the category of Soergel bimodules in arbitrary types. Secondly, we introduce the notion of derived horizontal trace of a monoidal dg category and compute the derived horizontal trace of Soergel bimodules in type A. As an application we obtain a derived annular Khovanov-Rozansky link invariant with an action of full twist insertion, and thus a categorification of the HOMFLY-PT skein module of the solid torus.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87749954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
A Survey of the Impact of Thurston’s Work on Knot Theory 论瑟斯顿对结理论的影响
arXiv: Geometric Topology Pub Date : 2020-02-03 DOI: 10.1007/978-3-030-55928-1_3
M. Sakuma
{"title":"A Survey of the Impact of Thurston’s Work on Knot Theory","authors":"M. Sakuma","doi":"10.1007/978-3-030-55928-1_3","DOIUrl":"https://doi.org/10.1007/978-3-030-55928-1_3","url":null,"abstract":"","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75508250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Classification of non-free Kleinian groups generated by two parabolic transformations 由两次抛物变换生成的非自由Kleinian群的分类
arXiv: Geometric Topology Pub Date : 2020-01-27 DOI: 10.1090/TRAN/8246
Hirotaka Akiyoshi, Ken'ichi Ohshika, J. Parker, M. Sakuma, H. Yoshida
{"title":"Classification of non-free Kleinian groups generated by two parabolic transformations","authors":"Hirotaka Akiyoshi, Ken'ichi Ohshika, J. Parker, M. Sakuma, H. Yoshida","doi":"10.1090/TRAN/8246","DOIUrl":"https://doi.org/10.1090/TRAN/8246","url":null,"abstract":"We give a full proof to Agol's announcement on the classification of non-free Kleinian groups generated by two parabolic transformations.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":" 41","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91515729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Automorphisms of Contact Graphs of CAT(0) Cube Complexes CAT(0)立方配合物接触图的自同构
arXiv: Geometric Topology Pub Date : 2020-01-23 DOI: 10.1093/imrn/rnaa280
Elia Fioravanti
{"title":"Automorphisms of Contact Graphs of CAT(0) Cube Complexes","authors":"Elia Fioravanti","doi":"10.1093/imrn/rnaa280","DOIUrl":"https://doi.org/10.1093/imrn/rnaa280","url":null,"abstract":"We show that, under weak assumptions, the automorphism group of a ${rm CAT(0)}$ cube complex $X$ coincides with the automorphism group of Hagen's contact graph $mathcal{C}(X)$. The result holds, in particular, for universal covers of Salvetti complexes, where it provides an analogue of Ivanov's theorem on curve graphs of non-sporadic surfaces. This highlights a contrast between contact graphs and Kim-Koberda extension graphs, which have much larger automorphism group. We also study contact graphs associated to Davis complexes of right-angled Coxeter groups. We show that these contact graphs are less well-behaved and describe exactly when they have more automorphisms than the universal cover of the Davis complex.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"70 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82425472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Genericity of pseudo-Anosov mapping classes, when seen as mapping classes 伪anosov映射类的泛型，当被视为映射类时
arXiv: Geometric Topology Pub Date : 2020-01-10 DOI: 10.4171/LEM/66-3/4-6
V. Erlandsson, J. Souto, Jing Tao
{"title":"Genericity of pseudo-Anosov mapping classes, when seen as mapping classes","authors":"V. Erlandsson, J. Souto, Jing Tao","doi":"10.4171/LEM/66-3/4-6","DOIUrl":"https://doi.org/10.4171/LEM/66-3/4-6","url":null,"abstract":"We prove that pseudo-Anosov mapping classes are generic with respect to certain notions of genericity reflecting that we are dealing with mapping classes.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83381514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Quandle Module Quivers Quandle模块颤抖
arXiv: Geometric Topology Pub Date : 2019-12-28 DOI: 10.1142/s0218216520500844
Karma Istanbouli, Sam Nelson
{"title":"Quandle Module Quivers","authors":"Karma Istanbouli, Sam Nelson","doi":"10.1142/s0218216520500844","DOIUrl":"https://doi.org/10.1142/s0218216520500844","url":null,"abstract":"We enhance the quandle coloring quiver invariant of oriented knots and links with quandle modules. This results in a two-variable polynomial invariant with specializes to the previous quandle module polynomial invariant as well as to the quandle counting invariant. We provide example computations to show that the enhancement is proper in the sense that it distinguishes knots and links with the same quandle module polynomial.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"88 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76400343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Combinatorial random knots 组合随机结
arXiv: Geometric Topology Pub Date : 2019-12-13 DOI: 10.2140/involve.2020.13.633
Andrew Ducharme, E. Peters
{"title":"Combinatorial random knots","authors":"Andrew Ducharme, E. Peters","doi":"10.2140/involve.2020.13.633","DOIUrl":"https://doi.org/10.2140/involve.2020.13.633","url":null,"abstract":"We explore free knot diagrams, which are projections of knots into the plane which don't record over/under data at crossings. We consider the combinatorial question of which free knot diagrams give which knots and with what probability. Every free knot diagram is proven to produce trefoil knots, and certain simple families of free knots are completely worked out. We make some conjectures (supported by computer-generated data) about bounds on the probability of a knot arising from a fixed free diagram being the unknot, or being the trefoil.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82396592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Surgery obstructions and character varieties 手术障碍与特征变化
arXiv: Geometric Topology Pub Date : 2019-12-04 DOI: 10.1090/tran/8596
Steven Sivek, Raphael Zentner
{"title":"Surgery obstructions and character varieties","authors":"Steven Sivek, Raphael Zentner","doi":"10.1090/tran/8596","DOIUrl":"https://doi.org/10.1090/tran/8596","url":null,"abstract":"We provide infinitely many rational homology 3-spheres with weight-one fundamental groups which do not arise from Dehn surgery on knots in $S^3$. In contrast with previously known examples, our proofs do not require any gauge theory or Floer homology. Instead, we make use of the $SU(2)$ character variety of the fundamental group, which for these manifolds is particularly simple: they are all $SU(2)$-cyclic, meaning that every $SU(2)$ representation has cyclic image.","PeriodicalId":8454,"journal":{"name":"arXiv: Geometric Topology","volume":"127 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88698991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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