Strongly n-trivial Knots

Hugh Howards; John Luecke

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Strongly n-trivial Knots

Hugh Howards·John Luecke

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Abstract

A knot k is called ``strongly (n-1)-trivial.'' if there exists a projection of k, such that one can choose n crossings of the projection with the property that making the crossing changes corresponding to any of the $2^{n}-1$ nontrivial combinations of the selected crossings turns the original knot into the unknot. We prove that given any non-trivial knot k of genus g, k fails to be strongly n-trivial for all $n, n \geq 3g-1$.

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BibTeX RIS

Hugh Howards, John Luecke. 2000-04-28. Strongly n-trivial Knots. https://arxiv.org/abs/math/0004183

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