Geodesic
Brunnian links are determined by their complements
Mangum, Brian S1 ; Stanford, Theodore2
1Barnard College, Columbia University, Department of Mathematics, New York NY 10027, USA
2New Mexico State University, Department of Mathematical Sciences, Las Cruces NM 88003, USA
Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 143-152
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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.

DOI : 10.2140/agt.2001.1.143
Keywords: Brunnian, knot, link, link equivalence, link complement

Mangum, Brian S  1   ; Stanford, Theodore  2

1 Barnard College, Columbia University, Department of Mathematics, New York NY 10027, USA
2 New Mexico State University, Department of Mathematical Sciences, Las Cruces NM 88003, USA 
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Mangum, Brian S; Stanford, Theodore. Brunnian links are determined by their complements. Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 143-152. doi: 10.2140/agt.2001.1.143

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