Boring split links

• Autores: Scott A. Taylor
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 241, Nº 1, 2009, págs. 127-168
• Idioma: inglés
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• Resumen

  • Boring is an operation that converts a knot or two-component link in a 3-manifold into another knot or two-component link. It generalizes rational tangle replacement and can be described as a type of 2-handle attachment. Sutured manifold theory is used to study the existence of essential spheres and planar surfaces in the exteriors of knots and links obtained by boring a split link. It is shown, for example, that if the boring operation is complicated enough, a split link or unknot cannot be obtained by boring a split link. Particular attention is paid to rational tangle replacement. If a knot is obtained by rational tangle replacement on a split link, and a few minor conditions are satisfied, the number of boundary components of a meridional planar surface is bounded below by a number depending on the distance of the rational tangle replacement. This result is used to give new proofs of two results of Eudave-Muñoz and Scharlemann�s band sum theorem.