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Jones, Matt; Scharlemann, Martin

How a strongly irreducible Heegaard splitting intersects a handlebody. (English) Zbl 0974.57011

Topology Appl. 110, No. 3, 289-301 (2001).
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

Citations:

Zbl 0632.57010; Zbl 0926.57018
PDFBibTeX XMLCite
\textit{M. Jones} and \textit{M. Scharlemann}, Topology Appl. 110, No. 3, 289--301 (2001; Zbl 0974.57011)
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References:

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