Self C_k-move, quasi self C_k-move and the conway potential function for links

Nakanishi and Shibuya gave a relation between link homotopy and quasi self delta-equivalence. And they also gave a necessary condition for two links to be self delta-equivalent by using the multivariable Alexander polynomial. Link homotopy and quasi self delta-equivalence are also called self C ₁-equivalence and quasi self C₂-equivalence respectively. In this paper, we generalize their results. In Sec. 1, we give a relation between self C_k-equivalence and quasi self C_k+1- equivalence. In Secs. 2 and 3, we give necessary conditions for two links to be self C_k-equivalent by using the multivariable Conway potential function and the Conway polynomial respectively.