Brunnian links

Brunnian links are determined by their complements

If L1 and L2 are two Brunnian links with all pairwise linking numbers 0, then we show that L1 and L2 are equivalent if and only if they have homeomorphic complements. In particular, this holds for all Brunnian links with at least three components. If L1 is a Brunnian link with all pairwise linking numbers 0, and the complement of L2 is homeomorphic to the complement of L1 , then we show that L2...

On the colored Jones polynomials of ribbon links, boundary links and Brunnian links

Habiro gave principal ideals of Z[q, q−1] in which certain linear combinations of the colored Jones polynomials of algebraically-split links take values. The author proved that the same linear combinations for ribbon links, boundary links and Brunnian links are contained in smaller ideals of Z[q, q−1] generated by several elements. In this paper, we prove that these ideals also are principal, e...

Finite Type Invariants and Milnor Invariants for Brunnian Links

A link L in the 3-sphere is called Brunnian if every proper sublink of L is trivial. In a previous paper, the first author proved that the restriction to Brunnian links of any Goussarov-Vassiliev finite type invariant of (n + 1)component links of degree < 2n is trivial. The purpose of this paper is to study the first nontrivial case. We show that the restriction of an invariant of degree 2n to ...

An Infinite Family of Convex Brunnian Links in R

This paper proves that convex Brunnian links exist for every dimension n ≥ 3 by constructing explicit examples. These examples are three-component links which are higher-dimensional generalizations of the Borromean rings. Figure 1. The Borromean Rings

Brunnian Spheres