Primeness of Links
Yasutaka Nakanishi · Institutional Repositories DataBase (IRDB) · 1981
introduce the method of tangles to prove the primeness of certain knots.In Section 1, we will generalize a notation of tangles and obtain a more applicable machine to links.For examples, we will easily see that some links are Brunnian in Section 2.We know in [11] that any link is concordant to a prime link with the same Alexander invariant.In Section 3, we will show that any n-components link (n~2) is concordant to a prime link with the same Alexander invariant preserving the knot types of components and the double of this concordance is ambient isotopic to the direct product.F. Hosokawa [ 5] defines V-polynomials of links and characterizes them as reciprocal polynomials of even degree.In Section 4, we wi 11 characterize V-polynomials of ribbon (slice) links in the weak sense as reciprocal polynomials of even degree.In Section 5, we will elementarily prove "For each integer n, there are distinct prime knots with the same n-fold cyclic branched covering space.11 This paper should be interpret in the piecewise-linear category.The standard results and definitions of the link theory is reffered to D.