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Compressing thin spheres in the complement of a link
Journal article   Open access   Peer reviewed

Compressing thin spheres in the complement of a link

Maggy Tomova
Topology and its applications, Vol.153(15), pp.2987-2999
2006
DOI: 10.1016/j.topol.2006.01.006
url
https://doi.org/10.1016/j.topol.2006.01.006View
Published (Version of record) Open Access

Abstract

Let L be a link in S 3 that is in thin position but not in bridge position and let P be a thin level sphere with compressing disk D. We introduce the idea of alternating level spheres for D and show that all such spheres are thin and their widths are monotone decreasing. This allows us to generalize a result of Wu by giving a bound on the number of disjoint irreducible compressing disks P can have in terms of the width of P, including identifying thin spheres with unique compressing disks. We also give conditions under which P must be incompressible on some side or be weakly incompressible. In particular we show that the thin level sphere of second lowest width is weakly incompressible. If P is strongly compressible we describe how a pair of compressing disks must lie relative to the link.
Compressing disks Thin spheres Weakly incompressible

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