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2001 Brunnian links are determined by their complements
Brian S Mangum, Theodore Stanford
Algebr. Geom. Topol. 1(1): 143-152 (2001). DOI: 10.2140/agt.2001.1.143

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.

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Brian S Mangum. Theodore Stanford. "Brunnian links are determined by their complements." Algebr. Geom. Topol. 1 (1) 143 - 152, 2001. https://doi.org/10.2140/agt.2001.1.143

Information

Received: 16 November 2000; Accepted: 28 February 2001; Published: 2001
First available in Project Euclid: 21 December 2017

zbMATH: 0970.57002
MathSciNet: MR1823496
Digital Object Identifier: 10.2140/agt.2001.1.143

Subjects:
Primary: 57M25
Secondary: 57M27

Rights: Copyright © 2001 Mathematical Sciences Publishers

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