Brunnian links are determined by their complements

Ted Stanford

KNOTS in WASHINGTON 10 Japan-USA; workshop in Knot Theory
January 23-30, 2000
George Washington University
Washington, DC, USA

Organizers
Kazuaki Kobayashi, Jozef H. Przytycki, Yongwu Rong, Kouki Taniyama, Tatsuya Tsukamoto, Akira Yasuhara

Conference Homepage

Brunnian links are determined by their complements
by
Ted Stanford
United States Naval Academy
Coauthors: Brian Mangum (Barnard College, Columbia University)

If L₁ and L₂ are two Brunnian links with all pairwise linking numbers 0, then 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 L₂ may be obtained from L₁ by a sequence of twists around unknotted components. These results lead to a straightforward way of reducing the problem of detecting a trivial link to the problems of detecting and straightening out a trivial knot.

http://front.math.ucdavis.edu/math.GT/9912006

Date received: January 14, 2000