The Link Group Presentation Of Several Kinds Of Framed Links

In this paper,we study the link group presentation of several kinds of tramed links.Given an oriented alternating knot K,denoting K1-K,K2 is a copy of K being pushed away from K along the direction f×tK(f is a smooth nonzero normal vector field defined on a small neighborhood of K,let tK be the tangent vector field on K).We obtain K3,K4,...,Kn in the same way,denoting Ln={K1,K2,...,Kn}.We care about the presentation of link group G(Ln).This article gives a recursion formula for the Wirtinger presentation of G{Ln).Then,according to the formula,we analyze the Wirtinger presentation of G(Ln)and G(Ln+1),how their numbers and relations of generators change.Finally,we generalize that framed links given by alternating knot,when adding a copy,its increased generators of the corresponding link group and generators of ?1(R3-K)have the same number.