How a strongly irreducible Heegaard splitting intersects a handlebody

Abstract

It has been shown elsewhere that a strongly irreducible Heegaard splitting surface Q of a compact orientable 3-manifold M can, under reasonable side conditions, intersect a ball or a solid torus in M in only a few possible ways. Here we extend those results to describe how Q can intersect a handlebody in M.

13 pages, 5 figures