Cut-disks for level spheres in link and tangle complements

2008/01/12 by Maggy Tomova, Tomova, Maggy
Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25

paper · pdf · doi:10.48550/arxiv.0801.1898

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

arxiv created 2008/04/30 · arxiv updated 2009/12/01

Abstract

Wu has shown that if a link or a knot L in S³ 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 ⊂ S³ 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 S² × [-1,1].

Related

• Compressing thin spheres in the complement of a link
• Non-parallel essential surfaces in knot complements
• A note on the nearly additivity of knot width
• Standard position for surfaces in link complements in arbitrary 3-manifolds
• Note on surface-link of trivial components