# A distance for circular Heegaard splittings

title={A distance for circular Heegaard splittings},
author={Kevin Lamb and Patrick Weed},
journal={Journal of Knot Theory and Its Ramifications},
year={2019}
}
• Published 17 December 2018
• Mathematics
• Journal of Knot Theory and Its Ramifications
For a knot [Formula: see text], its exterior [Formula: see text] has a singular foliation by Seifert surfaces of [Formula: see text] derived from a circle-valued Morse function [Formula: see text]. When [Formula: see text] is self-indexing and has no critical points of index 0 or 3, the regular levels that separate the index-1 and index-2 critical points decompose [Formula: see text] into a pair of compression bodies. We call such a decomposition a circular Heegaard splitting of [Formula: see…

## References

SHOWING 1-10 OF 25 REFERENCES
Circular Thin Position for Knots in S
A regular circle-valued Morse function on the knot complement CK = S 3 \ K is a function f : CK → S 1 which separates critical points and which behaves nicely in a neighborhood of the knot. Such a
Circular thin position for knots in the 3-sphere
A regular circle-valued Morse function on the knot complement C(K) = S^3\K is a function f from C(K) to S^1 which separates critical points and which behaves nicely in a neighborhood of the knot.
The topology of 3-manifolds, Heegaard distance and the mapping class group of a 2-manifold
We have had a long-standing interest in the way that structure in the mapping class group of a surface reflects corresponding structure in the topology of 3-manifolds, and conversely. We find this
Distance and bridge position
• Mathematics
• 2003
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
Heegaard splittings of Haken manifolds have bounded distance
Given a Heegaard splitting and an incompressible surface S and a Heegaard splitting of an irreducible manifold, I shall use a generalization of Haken's lemma proved by Kobayashi in order to define a
Heegaard splittings and open books
We show that if the monodromy of an open book decomposition has sufficiently high displacement distance, acting on the loop and arc complex for a page, then it is the unique minimal Euler
Alternate Heegaard genus bounds distance
• Mathematics
• 2006
Suppose M is a compact orientable irreducible 3-manifold with Heegaard splitting surfaces P and Q. Then either Q is isotopic to a possibly stabilized or boundary-stabilized copy of P or the distance