Trunk of satellite and companion knots

摘要

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 1/2 is necessary in our second result trunk(K) > 1/2 m . trunk(J) as m >= n. We also discuss generalizations of the second result. (C) 2020 Elsevier B.V. All rights reserved.