In this note, we will study Delta link homotopy, which is an equivalence relation of ordered and oriented link types. Previously, a necessary condition was given by a pair of numerical invariants derived from the Conway polynomials for two link types to be Delta link homotopic. In this note, we will show that, for two component links, if their pairs of numerical invariants coincide then the two links are Delta link homotopic.
Yasutaka NAKANISHI. Yoshiyuki OHYAMA. "Delta link homotopy for two component links, III." J. Math. Soc. Japan 55 (3) 641 - 654, July, 2003. https://doi.org/10.2969/jmsj/1191418994