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.
Funding Statement
This work is partially supported by the project AlMaRe (ANR-19-CE40-0001-01) of the ANR.
Citation
Emmanuel GRAFF. "On braids and links up to link-homotopy." J. Math. Soc. Japan Advance Publication 1 - 35, May, 2023. https://doi.org/10.2969/jmsj/90449044
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