Accidental surfaces in knot complements

Geodesic Surfaces in Knot Complements

C-incompressible Planar Surfaces in Knot Complements

In [6] Wu shows 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 cut-disks. We also prove an analogous result for a specific kind of tangles in

Non-parallel Essential Surfaces in Knot Complements

We show that if a knot or link has n thin levels when put in thin position then its exterior contains a collection of n disjoint, non-parallel, planar, meridional, essential surfaces. A corollary is that there are at least n/3 tetrahedra in any triangulation of the complement of such a knot.

Incompressible surfaces in 2-bridge knot complements

To each rational number p/q, with q odd, there is associated the 2-bridge knot Kp/q shown in Fig. 1. QI bl Fig. 1. The 2-bridge knot Kp/q In (a), the central grid consists of lines of slope +p/q, which one can imagine as being drawn on a square "pillowcase". In (b) this "pillowcase" is punctured and flattened out onto a plane, making the two "bridges" more evident. The knot drawn is K3/5, which...

Meridional Almost Normal Surfaces in Knot Complements

Suppose K is a knot in a closed 3-manifold M such that M −N(K) is irreducible. We show that for any integer b there exists a triangulation of M −N(K) such that any weakly incompressible bridge surface for K of b bridges or fewer is isotopic to an almost normal bridge surface.