Natural properties of the trunk of a knot

Derek Davies; Alexander Zupan

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arXiv · 1608.00019

Natural properties of the trunk of a knot

Derek Davies·Alexander Zupan

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Abstract

The trunk of a knot in $S^3$, defined by Makoto Ozawa, is a measure of geometric complexity similar to the bridge number or width of a knot. We prove that for any two knots $K_1$ and $K_2$, we have $tr(K_1 \# K_2) = \max\{tr(K_1),tr(K_2)\}$, confirming a conjecture of Ozawa. Another conjecture of Ozawa asserts that any width-minimizing embedding of a knot $K$ also minimizes the trunk of $K$. We produce several families of probable counterexamples to this conjecture.

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BibTeX RIS

Derek Davies, Alexander Zupan. 2016-07-29. Natural properties of the trunk of a knot. https://arxiv.org/abs/1608.00019

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