On braids and links up to link-homotopy

Emmanuel Graff

doi:10.2969/jmsj/90449044

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arXiv · 2210.01539

On braids and links up to link-homotopy

Emmanuel Graff

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Abstract

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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Emmanuel Graff. 2022-10-04. On braids and links up to link-homotopy. https://doi.org/10.2969/jmsj%2F90449044

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