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Comparing Heegaard and JSJ structures of orientable 3-manifolds. (English) Zbl 0959.57010
The authors prove that the Heegaard genus of an irreducible closed orientable 3-manifold limits the number and complexity of the pieces that arise in the Jaco-Shalen-Johannson decomposition of the manifold by its canonical tori. Some earlier work in this direction was done by T. Kobayashi [Osaka J. Math. 24, 173-215 (1987; Zbl 0665.57010)].
Reviewer: J.Hebda (St.Louis)

MSC:
57M50 General geometric structures on low-dimensional manifolds
57N10 Topology of general \(3\)-manifolds (MSC2010)
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