Cut-disks for level spheres in link and tangle complements

Details Cut-disks for level spheres in link and tangle complements Cut-disks for level spheres in link and tangle complements

2008-01-12

arxiv.org/abs/0801.1898v3

Mathematics

Geometric Topology

18 pages, 10 figures. The main theorem has been modified to include an additional hypothesis

Scientific paper

Wu has shown that if a link or a knot $L$ in $S^3$ in thin position has thin spheres, then the thin sphere of lowest width is an essential surface in the link complement. In this paper we show that if we further assume that $L \subset S^3$ is prime, then the thin sphere of lowest width also does not have any vertical cut-disks. We also prove the result for a specific kind of tangles in $S^2 \times [-1,1]$.

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