On the hull numbers of torus links

Details On the hull numbers of torus links On the hull numbers of torus links

2004-12-07

arxiv.org/abs/math/0412139v1

Mathematics

Geometric Topology

14 pages

Scientific paper

The n-th hull of a union of curves in R^3 is the set of points with the property: Any plane passing through the point intersects the curves at least 2n times. The hull number u(L) of a link L is defined as the minimum number of non-empty hulls a representative of L can have. We show that the hull numbers of torus links are smaller than expected, but still large. In particular, for a link of type (p,p) hull number equals 3p/5, and in general for the type (p,q) with q>p it is greater than or equal to p/2.

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