The Dabkowski-Sahi invariant and $4$-moves for links

Haruko A. Miyazawa; Kodai Wada; Akira Yasuhara

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arXiv · 2005.11793

The Dabkowski-Sahi invariant and $4$-moves for links

Haruko A. Miyazawa·Kodai Wada·Akira Yasuhara

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Abstract

Dabkowski and Sahi defined an invariant of a link in the $3$-sphere, which is preserved under $4$-moves. This invariant is a quotient of the fundamental group of the complement of the link. It is generally difficult to distinguish the Dabkowski-Sahi invariants of given links. In this paper, we give a necessary condition for the existence of an isomorphism between the Dabkowski-Sahi invariant of a link and that of the corresponding trivial link. Using this condition, we provide a practical obstruction to a link to be trivial up to $4$-moves.

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Haruko A. Miyazawa, Kodai Wada, Akira Yasuhara. 2020-05-24. The Dabkowski-Sahi invariant and $4$-moves for links. https://arxiv.org/abs/2005.11793

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