Burnside groups and 𝑛-moves for links

Miyazawa, Haruko; Wada, Kodai; Yasuhara, Akira

doi:10.1090/proc/14470

Burnside groups and $n$-moves for links
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by Haruko A. Miyazawa, Kodai Wada and Akira Yasuhara PDF

Proc. Amer. Math. Soc. 147 (2019), 3595-3602 Request permission

Abstract:

M. K. Da̧bkowski and J. H. Przytycki introduced the $n$th Burnside group of a link, which is an invariant preserved by $n$-moves. Using this invariant, for an odd prime $p$, they proved that there are links which cannot be reduced to trivial links via $p$-moves. It is generally difficult to determine if $p$th Burnside groups associated to a link and the corresponding trivial link are isomorphic. In this paper, we give a necessary condition for the existence of such an isomorphism. Using this condition we give a simple proof for their results that concern $p$-move reducibility of links.

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