Incompressible Surfaces In Almost Alternating Knot Exteriors

Let K be an alternating knot or almost alternating knot, FS-K be an incompressible pair-wise incompressible surface. This paper studied the properties of F by discussing the properties of F S. For alternating knot, the genus of F equals zero when the component of F is less than eight. Then we generalized the result: the genus of F equals zero if only the topological graph of F is special simple. For almost alternating knot, we proved that the genus of F equals zero when the number of components of F is less than eight.