Locally unknotted spines of Heegaard splittings

  title={Locally unknotted spines of Heegaard splittings},
  author={Jesse Johnson},
  journal={Algebraic \& Geometric Topology},
  • Jesse Johnson
  • Published 2004
  • Mathematics
  • Algebraic & Geometric Topology
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 

Figures from this paper

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- denceExpand
Short geodesics in hyperbolic 3-manifolds
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 $M$ andExpand
A proof of Waldhausen's uniqueness of splittings of $S^3$ (after Rubinstein and Scharlemann)
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 theirExpand


Local detection of strongly irreducible Heegaard splittings
Abstract Let S be a Heegaard splitting surface of a compact orientable 3-manifold M . If S is strongly irreducible, the manner in which it can intersect a ball or a solid torus in M is veryExpand
Reducing heegaard splittings
Abstract If a Heegaard splitting of a nonsufficiently large 3-manifold has the property that there exist essential disks, one in each of the two Heegaard handlebodies, whose boundaries are disjoint,Expand
Comparing Heegaard splittings of non-haken 3-manifolds
Abstract Cerf theory can be used to compare two strongly irreducible Heegaard splittings of the same closed orientable 3-manifold. Any two splitting surfaces can be isotoped so that they intersect inExpand
Algebraic & Geometric Topology
  • Algebraic & Geometric Topology
  • 2005
CA 95616, USA Email: jjohnson@math.ucdavis.edu Received
  • CA 95616, USA Email: jjohnson@math.ucdavis.edu Received
  • 2005
Reducing Heegaard splittings, Topology Appl
  • Reducing Heegaard splittings, Topology Appl
  • 1987
Sur les difféomorphismes de la sphère de dimension trois (Γ4 = o)