Abstract

We study the knot invariant called trunk, as defined by Ozawa [7], and the relation of the trunk of a satellite knot with the trunk of its companion knot. Our first result is trunk(K)≥n⋅trunk(J) where trunk(⋅) denotes trunk of a knot, K is a satellite knot with companion J, and n is the winding number of K. To upgrade winding number to wrapping number, denoted by m, an extra factor of 12 is necessary in our second result trunk(K)>12m⋅trunk(J) as m≥n. We also discuss generalizations of the second result.

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