Strongly n-trivial Knots

Details Strongly n-trivial Knots Strongly n-trivial Knots

2000-04-28

arxiv.org/abs/math/0004183v1

Mathematics

Geometric Topology

10 pages, 3 figures

Scientific paper

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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