Distance and bridge position

• Autores: David Bachman, Saul Schleimer
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 219, Nº 2, 2005, págs. 221-236
• Idioma: inglés
• DOI: 10.2140/pjm.2005.219.221
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• Resumen

  • J. Hempel's denition of the distance of a Heegaard surface generalizes to a notion of complexity for any knot that is in bridge position with respect to a Heegaard surface. Our main result is that the distance of a knot in bridge position is bounded above by twice the genus, plus the number of boundary components, of an essential surface in the knot complement. As a consequence knots constructed via suciently high powers of pseudo-Anosov maps have minimal bridge presentations which are thin.