Algebraic & Geometric Topology 1 (2001) 143–152

DOI: 10.2140/agt.2001.1.143

arXiv: math.GT/9912006

Abstract

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 may be obtained from L₁ by a sequence of twists around unknotted components. Finally, we show that for any positive integer n, an algorithm for detecting an n–component unlink leads immediately to an algorithm for detecting an unlink of any number of components. This algorithmic generalization is conceptually simple, but probably computationally impractical.

Keywords

Brunnian, knot, link, link equivalence, link complement

Mathematical Subject Classification

Primary: 57M25

Secondary: 57M27

References

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Publication

Received: 16 November 2000
Accepted: 28 February 2001
Published: 2 March 2001

Authors