Distance and bridge position

By David Bachman, Saul Schleimer. 2003

61 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/316aa0c56f14a2ffd60b985bc1bca0abe92a52ae

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Maggy Tomova
2. Msri Postdoctoral Fellow
3. Tao Li

In Mathematical Physics

1. Maggy Tomova
2. Msri Postdoctoral Fellow
3. Tao Li

Citations in the corpus

• Multiple bridge surfaces restrict knot distance (2005, methodology): “Now we can recover the bound on distance obtained in [2] but us ing our definition of distance.”
• Geometric (2019, methodology): “Here in this study, we recorded neuronal activity in the V2 to elucidate how the sensory manifold, where MIC orientations remains linearly inseparable akin to the stimulus space, transforms into the perceptual manifold that affords linear separability.”