# Locally unknotted spines of Heegaard splittings

@article{Johnson2004LocallyUS, title={Locally unknotted spines of Heegaard splittings}, author={Jesse Johnson}, journal={Algebraic \& Geometric Topology}, year={2004}, volume={5}, pages={1573-1584} }

We show that under reasonable conditions, the spines of the handlebodies of a strongly irreducible Heegaard splitting will intersect a closed ball in a graph which is isotopic into the boundary of the ball. This is in some sense a generalization of the results by Scharlemann on how a strongly irreducible Heegaard splitting surface can intersect a ball. AMS Classification 57M27; 57Q10

#### 3 Citations

HORIZONTAL HEEGAARD SPLITTINGS OF SEIFERT FIBERED SPACES

- Mathematics
- 2008

We show that if an orientable Seifert fibered space M with an orientable genus g base space admits a strongly irreducible horizontal Heegaard splitting then there is a one-to-one correspon- dence… Expand

Short geodesics in hyperbolic 3-manifolds

- Mathematics
- 2009

For each $g \ge 2$, we prove existence of a computable constant $\epsilon(g) > 0$ such that if $S$ is a strongly irreducible Heegaard surface of genus $g$ in a complete hyperbolic 3-manifold $M$ and… Expand

A proof of Waldhausen's uniqueness of splittings of $S^3$ (after Rubinstein and Scharlemann)

- Mathematics
- 2006

In [Topology 35 (1996) 1005--1023] J H Rubinstein and M Scharlemann, using Cerf Theory, developed tools for comparing Heegaard splittings of irreducible, non-Haken manifolds. As a corollary of their… Expand

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