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- W1988384501 abstract "A knot K is called n -adjacent to the unknot, if K admits a projection containing n generalized crossings such that changing any 0< m ⩽ n of them yields a projection of the unknot. We show that a non-trivial satellite knot K is n -adjacent to the unknot, for some n >0, if and only if it is n -adjacent to the unknot in any companion solid torus. In particular, every model knot of K is n -adjacent to the unknot. Along the way of proving these results, we also show that 2-bridge knots of the form K p / q , where p / q =[2 q 1 ,2 q 2 ] for some q 1 ,q 2 ∈ Z , are precisely those knots that have genus one and are 2-adjacent to the unknot." @default.
- W1988384501 created "2016-06-24" @default.
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- W1988384501 date "2004-03-01" @default.
- W1988384501 modified "2023-09-29" @default.
- W1988384501 title "Knot adjacency and satellites" @default.
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- W1988384501 doi "https://doi.org/10.1016/j.topol.2003.08.001" @default.
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