关于辫状和链状的链同伦

Pub Date : 2022-10-04 DOI:10.2969/jmsj/90449044

Emmanuel Graff

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引用次数: 0

摘要

本文从Habiro的clacker演算的角度研究了链接和辫状到链接的伦理学。更准确地说，我们在两个主要方向上使用了claser同伦学。首先，我们定义并计算了一个忠实的线性表示的同伦辫群，通过使用clasers作为几何交换子。其次，我们给出了Levine将4分量链接分类到链接同构的几何证明，并进一步讨论了代数分裂情况下5分量链接的分类。

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On braids and links up to link-homotopy

This paper deals with links and braids up to link-homotopy, studied from the viewpoint of Habiro's clasper calculus. More precisely, we use clasper homotopy calculus in two main directions. First, we define and compute a faithful linear representation of the homotopy braid group, by using claspers as geometric commutators. Second, we give a geometric proof of Levine's classification of 4-component links up to link-homotopy, and go further with the classification of 5-component links in the algebraically split case.

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