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How a strongly irreducible Heegaard splitting intersects a handlebody. (English) Zbl 0974.57011
The notion of a strongly irreducible Heegaard splitting was introduced by A. J. Casson and 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.
Reviewer: J.Hebda (St.Louis)
##### MSC:
 57N10 Topology of general $$3$$-manifolds (MSC2010) 57M50 General geometric structures on low-dimensional manifolds
##### Keywords:
weakly incompressible
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##### References:
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