Delta link homotopy for two component links. III. (English) Zbl 1030.57016

Nakanishi, Yasutaka; Ohyama, Yoshiyuki

J. Math. Soc. Japan 55, No. 3, 641-654 (2003).

Summary: We study Delta link homotopy, which is an equivalence relation of ordered and oriented link types. In two previous paper, [Y. Nakanishi, Topology Appl. 121, 169-182 (2002; Zbl 1001.57013) and Y. Nakamishi and Y. Ohyama, J. Knot Theory Ramifications 11, 353-362 (2002; Zbl 1005.57003)] 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 show that, for two component links, if these numerical invariants coincide then the two links are Delta link homotopic.

MSC:

57M25

Knots and links in the \(3\)-sphere (MSC2010)

Keywords:

Conway polynomial; Vassiliev invariant; Delta link homotopy

Citations:

Zbl 1001.57013; Zbl 1005.57003