Incompressible,Pairwisely Incompressible Surfaces in Alternating Knot Complements

Abstract:

      In this paper, we deal with incompressible、pairwise incompressible surfaces in alternating complements by using twist crossing number. Let K be a prime alternating knot,F?Ｓ^３-K is a incompressible、pairwise incompressible surface. If TCN(K)≤5(TCN=twist crossing number), then F is a punctured sphere.