Incompressible surfaces in knot spaces

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

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...

Spaces of Incompressible Surfaces

The homotopy type of the space of PL homeomorphisms of a Haken 3 manifold was computed in [H1], and with the subsequent proof of the Smale conjecture in [H2], the computation carried over to diffeomorphisms as well. These results were also obtained independently by Ivanov [I1,I2]. The main step in the calculation in [H1], though not explicitly stated in these terms, was to show that the space o...

Closed Incompressible Surfaces of Genus Two in 3-bridge Knot Complements

In this paper, we characterize closed incompressible surfaces of genus two in the complements of 3-bridge knots and links. This characterization includes that of essential 2-string tangle decompositions for 3-bridge knots and links.

Geodesic Surfaces in Knot Complements