How a strongly irreducible Heegaard splitting intersects a handlebody (Q5928485)

The notion of a strongly irreducible Heegaard splitting was introduced by \textit{A. J. Casson} and \textit{C. McA. Gordon} [ibid. 27, 275-283 (1987; Zbl 0632.57010)]. In the paper under review, the authors show how a strongly irreducible Heegaard splitting surface \(Q\) of a 3-manifold \(M\) with extra side conditions intersects an arbitrary genus handlebody \(H\) in \(M\). In a previous paper [ibid. 90, No. 1-3, 135-147 (1998; Zbl 0926.57018)], the second author investigated the case when \(H\) is either a ball or solid torus. The side conditions imply that the surface is weakly incompressible, so that the problem becomes a problem in characterizing weakly incompressible surfaces embedded in a handlebody.