Efstratia Kalfagianni, Xiao-Song Lin
We show that for an $n$-component, $n$-bridge link and a positive integer $m$, the following is true: If the longitudes of $L$ lie in the $(m+2)$-th term of the lower central series of the link group then all the finite type invariants of orders $\leq m$ for $L$ are the same as these of the $n$-component unlink.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In his paper "On the Schlafli differential equality", J. Milnor conjectured that the volume of n-dimensional hyperbolic and spherical simplices, as a function of the dihedral angles, extends continuously to the closure of the space of allowable angles (``The continuity conjecture''), and furthermore, the limit at a boundary point is equal to 0 if and only if the point lies in the closure of the space of angles of Euclidean tetrahedra (``the Vanishing Conjecture''). A proof of the Continuity Conjecture was given by F. Luo -- Luo's argument uses Kneser's formula for the volume together with some…
We show that if a braid $B$ can be parametrised in a certain way, then previous work can be extended to a construction of a polynomial $f:\mathbb{R}^4\to\mathbb{R}^2$ with the closure of $B$ as the link of an isolated singularity of $f$, showing that the closure of $B$ is real algebraic. In particular, we prove that closures of squares of strictly homogeneous braids and certain lemniscate links are real algebraic. We also show that the constructed polynomials satisfy the strong Milnor condition, providing an explicit fibration of the complement of the closure of $B$ over $S^1$.
Passing from plat closure to standard closure of braids in $\mathbb{R}^3$, in handlebodies and in thickened surfaces
该研究提出一种可在辫子的plat闭包与标准闭包表示的同一纽结/链环间相互转换的算法，分析了三维欧氏空间、柄体、加厚曲面三种情形，并证明两类转换分别具有二次、线性的时间复杂度。
Milnor's inequality and circular elastic knots
本文推广Milnor不等式至纽结类的$C^1$-闭包，结合近期工作解决圆形弹性纽结猜想，证明当桥指数与辫指数相同时，多重覆盖圆为唯一弹性纽结。
A Markov theorem for plat closure of surface braids in Dunwoody and periodic Takahashi manifolds
本文针对Dunwoody与周期Takahashi流形中的链环，利用Heegaard分解和辫群plat闭包表示，提出算法确定并显式计算plat滑动等价移动，从而建立相应的Markov定理。
Plat closures of spherical braids in $\mathbb{R}P^3$
本文定义了球面辫子的平闭包以构造$\mathbb{R}P^3$中的链环，证明了所有链环均可如此实现，并给出分支数公式及一组类马尔可夫移动，其完备性待研究。
Closure of knitted surfaces and surface-links
该研究推广编织曲面提出针织曲面与二维针织物概念，证明任意曲面链同痕于二维针织物闭合，还证明2次针织曲面的plat闭合及2次二维针织物的闭合均等价于平凡曲面链。
In this paper, we give a complete set of finite type string link invariants of degree <5. In addition to Milnor invariants, these include several string link invariants constructed by evaluating knot invariants on certain closure of (cabled) string links. We show that finite type invariants classify string links up to C_k-moves for k<6, which proves, at low degree, a conjecture due to Goussarov and Habiro. We also give a similar characterization of finite type concordance invariants of degree <6.
We introduce the (general) homotopy groups of spheres as link invariants for Brunnian-type links through the investigations on the intersection subgroup of the normal closures of the meridians of strongly nonsplittable links. The homotopy groups measure the difference between the intersection subgroup and symmetric commutator subgroup of the normal closures of the meridians and give the invariants of the links obtained in this way. Moreover the higher homotopy-group invariants can produce some links that could not be detected by the Milnor invariants. Furthermore all homotopy groups of spheres…
The mixed Hilden braid group and the plat equivalence in handlebodies
本文证明亏格 g 柄体中的任意纽结或链环均可表示为辫子的 plat 闭包，定义混合 Hilden 辫子群，并给出同一链环同痕类下混合 plat 的代数等价判据。
On the classification of 2-plat 2-knots
本文研究2-plat 2-结的分类，引入新的不变量作为 torsion 不变量的类比，并作为2-结可逆性的障碍。
We study a certain type of braid closure which resembles the plat closure but has certain advantages; for example, it maps pure braids to knots. The main results of this note are a Markov-type theorem and a description of how Vassiliev invariants behave under this braid closure.
Bridge Positions and Plat Presentations of Links
本文建立纽结的桥位置与平台表示的Hilden双陪集类的对应关系，将平台表示的代数问题转化为桥位置的几何问题，重新确立相关结果并探讨其在辫子平台闭包研究中的应用。
Computation of the knot symmetric quandle and its application to the plat index of surface-links
该研究提出利用plat形式表示计算曲面链的纽结对称广群，并证明了对任意整数g≥0和m≥2，存在无穷多亏格为g且plat指数为m的不同曲面纽结。
We prove a Markov theorem for tame links in a connected closed orientable 3-manifold $M$ with respect to a plat-like representation. More precisely, given a genus $g$ Heegaard surface $Σ_g$ for $M$ we represent each link in $M$ as the plat closure of a braid in the surface braid group $B_{g,2n}=π_1(C_{2n}(Σ_g))$ and analyze how to translate the equivalence of links in $M$ under ambient isotopy into an algebraic equivalence in $B_{g,2n}$. First, we study the equivalence problem in $Σ_g\times [0,1]$, and then, to obtain the equivalence in $M$, we investigate how isotopies corresponding to "slidi…
We give a new definition of the knot invariant associated to the Lie algebra su_{N+1}. The knot or link must be presented as the plat closure of a braid. The invariant is then a homological intersection pairing between two submanifolds of a configuration space of points in a disk. This generalizes previous work on the Jones polynomial, which is the case N=1.
Knots and non-orientable surfaces in 3-manifolds
本文提出一种通过嵌入不可定向曲面表示3-流形中纽结与链环的新方法，将其表示为曲面辫群元素的类似于plat的闭包，并在透镜空间和平凡圆丛中给出示例。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。