Abstract
AbstractWe provide an algorithm to determine whether a link L admits a crossing change that turns it into a split link, under some fairly mild hypotheses on L. The algorithm also provides a complete list of all such crossing changes. It can therefore also determine whether the unlinking number of L is 1.
Funder
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
Reference54 articles.
1. Baker, K., Buck, D.: The classification of rational subtangle replacements between rational tangles. Algebr. Geom. Topol. 13, 1413–1463 (2013)
2. Bing, R.: A homeomorphism between the $$3$$-sphere and the sum of two solid horned spheres. Ann. Math. 2(56), 354–362 (1952)
3. Boileau, M., Leeb, B., Porti, J.: Geometrization of 3-dimensional orbifolds. Ann. Math. 162(1), 195–290 (2005)
4. Bonahon, F., Siebenmann, L.: The characteristic toric splitting of irreducible compact 3-orbifolds. Math. Ann. 278, 441–479 (1987)
5. Bonahon, F., Siebenmann, L.: New Geometric Splittings of Classical Knots and the Classification and Symmetries of Arborescent Knots, Preprint