Embedding tangles in links
Geometric Topology
2007-05-23 v1
Abstract
We reprove and extend a result of David Krebes (J. Knot Theory Ramif. 8 (1999), 321-352) giving an obstruction to embedding a tangle T into a link L. Closing the tangle up in the two obvious ways gives rise to two links, the numerator and denominator links n(T) and d(T). Applying a homological argument to the 2-fold branched covers of these links, we show that the gcd of the determinants of the numerator and denominator divides the determinant of L.
Keywords
Cite
@article{arxiv.math/0001141,
title = {Embedding tangles in links},
author = {Daniel Ruberman},
journal= {arXiv preprint arXiv:math/0001141},
year = {2007}
}
Comments
Latex; 8 pages, 2 figures. To appear in J. Knot Theory Ramif