Compressing thin spheres in the complement of a link

Details Compressing thin spheres in the complement of a link Compressing thin spheres in the complement of a link

2004-04-15

arxiv.org/abs/math/0404282v2

Mathematics

Geometric Topology

New results have been added including a bound on the number of disjoint irreducible compressing disks a thin sphere can have.

Scientific paper

Let L be a link in the 3-sphere that is in thin position but not in bridge position and let P be a thin level sphere. We generalize a result of Wu by giving a bound on the number of disjoint irreducible compressing disks that P can have, including identifying thin spheres with unique compressing disks. We also give conditions under which P must be incompressible on a particular side or be weakly incompressible. If P is strongly compressible we describe how a pair of compressing disks must lie relative to the link.

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