Tied links in S3 were introduced by Aicardi and Juyumaya as standard links in S3 equipped with some non-embedded arcs, called 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 monoids TMg,n by combining the algebraic mixed braid groups defined by Lambropoulou and the tied braid monoid, and we formulate and prove analogues of the Alexander and the Markov theorems for tied links in the 3-manifolds mentioned above. We also present an L-move braid equivalence for tied braids and we discuss further research related to tied links in knot complements and c.c.o. 3-manifolds. The theory of tied links has potential use in some aspects of molecular biology.

中文翻译：

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各种拓扑设置中的绑定链接

绑定的链接小号3由 Aicardi 和 Juyumaya 作为标准链接引入小号3配备了一些非嵌入的弧，称为领带，加入链接的一些组件。然后，弗洛雷斯自然地概括了 Solid Torus 中的绑定链接。在本文中，我们研究了其他拓扑设置中的这一类新链接。更准确地说，我们研究镜头空间中的绑定链接大号(p, 1), 在属的把手中G，并且在G-组件取消链接。我们介绍绑辫子幺半群吨米G,n通过结合由 Lambropoulou 定义的代数混合辫群和束缚辫幺半群，我们制定并证明了上述 3 流形中束缚链接的亚历山大定理和马尔可夫定理的类似物。我们还提出了一个大号-移动绑辫的编织等效性，我们讨论与结补和 cco 3 歧管中的绑链相关的进一步研究。联系的理论在分子生物学的某些方面具有潜在的用途。