Mathematics – Geometric Topology
Scientific paper
2009-05-27
Mathematics
Geometric Topology
11 pages, 3 figures. In v2, Theorem 1.9 was added
Scientific paper
We introduce two numerical invariants, the waist and the trunk of knots. The waist of a closed incompressible surface in the complement of a knot is defined as the minimal intersection number of all compressing disks for the surface in the 3-sphere and the knot. Then the waist of a knot is defined as the maximal waist of all closed incompressible surfaces in the complement of the knot. On the other hand, the trunk of a knot is defined as the minimal number of the intersection of the most thick level 2-sphere and the knot over all Morse positions of the knot. In this paper, we obtain an inequality between the waist and the trunk of knots and show that the inequality is best possible. We also define the supertrunk of a knot and relate it to the hull number and the 3-width.
Ozawa Makoto
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