论文标题
在各种拓扑设置中绑定的链接
Tied Links in various topological settings
论文作者
论文摘要
Aicardi和Juyumaya作为$ S^3 $中的绑定链接作为$ S^3 $中的标准链接，配备了一些非包装弧，称为{\ it ties}}，连接了该链接的某些组件。然后通过弗洛雷斯自然概括了固体圆环中的绑带链接。在本文中，我们研究了其他拓扑设置中的这一新链接。更确切地说，我们研究了镜头空间$ L（p，1）$的绑定链接，在属$ g $的手柄中，并在$ g $ - $ -COMPONTEND UNINK的补充中进行了补充。我们通过组合Lambropoulou和绑定的编织Monoid定义的代数混合编织组来介绍绑定的编织组$ tb_ {g，n} $，我们陈述并证明了亚历山大和马尔可夫定理，以在上面提到的3个manifolds中绑定了绑定的链接。最后，我们强调需要进一步的步骤，以研究结和C.C.O.中的绑定链接。 3个manifolds，这是续集纸的主题。
Tied links in $S^3$ were introduced by Aicardi and Juyumaya as standard links in $S^3$ equipped with some non-embedded arcs, called {\it ties}, joining some components of the link. Tied links in the Solid Torus were then naturally generalized by Flores. In this paper we study this new class of links in other topological settings. More precisely, we study tied links in the lens spaces $L(p,1)$, in handlebodies of genus $g$, and in the complement of the $g$-component unlink. We introduce the tied braid groups $TB_{g, n}$ by combining the algebraic mixed braid groups defined by Lambropoulou and the tied braid monoid, and we state and prove Alexander's and Markov's theorems for tied links in the 3-manifolds mentioned above. Finally, we emphasize on further steps needed in order to study tied links in knot complements and c.c.o. 3-manifolds, which is the subject of a sequel paper.
