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Classification of links up to self $#$-move

Tetsuo Shibuya·Akira Yasuhara
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Abstract

A pass-move and a $#$-move are local moves on oriented links defined by L.H. Kauffman and H. Murakami respectively. Two links are self pass-equivalent (resp. self $#$-equivalent) if one can be deformed into the other by pass-moves (resp. $#$-moves), where non of them can occur between distinct components of the link. These relations are equivalence relations on ordered oriented links and stronger than link-homotopy defined by J. Milnor. We give two complete classifications of links with arbitrarily many components up to self pass-equivalence and up to self $#$-equivalence respectively. So our classifications give subdivisions of link-homotopy classes.

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Tetsuo Shibuya, Akira Yasuhara. 2000-06-06. Classification of links up to self $#$-move. https://arxiv.org/abs/math/0006040

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