Meridional Almost Normal Surfaces in Knot Complements

Abstract

Suppose $K$ is a knot in a closed 3-manifold $M$ such that $\overline{M-N(K)}$ is irreducible. We show that for any positive integer $b$ there exists a triangulation of $\overline{M-N(K)}$ such that any weakly incompressible bridge surface for $K$ of $b$ bridges or fewer is isotopic to an almost normal bridge surface.

23 pages, 9 figures

References in corpus (2)

• Algorithmically detecting the bridge number of hyperbolic knots
• Almost normal Heegaard surfaces

Cited by in corpus (1)

• Algorithmically detecting the bridge number of hyperbolic knots