On the Heegaard splittings of amalgamated 3-manifolds

Abstract

We give a combinatorial proof of a theorem first proved by Souto which says the following. Let M_1 and M_2 be simple 3-manifolds with connected boundary of genus g>0. If M_1 and M_2 are glued via a complicated map, then every minimal Heegaard splitting of the resulting closed 3-manifold is an amalgamation. This proof also provides an algorithm to find a bound on the complexity of the gluing map.

arXiv commentThis is the version published by Geometry & Topology Monographs on 3 December 2007

References in corpus (3)

• Alternate Heegaard genus bounds distance
• Heegaard splittings of compact 3-manifolds
• Sweepouts of amalgamated 3-manifolds

Cited by in corpus (9)

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• Saddle tangencies and the distance of Heegaard splittings
• Degeneration of Heegaard genus, a survey
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• Additivity of Heegaard genera of bounded surface sums
• The Heegaard genus of bundles over S^1
• Heegaard structure respects complicated JSJ decompositions
• Stabilization, amalgamation, and curves of intersection of Heegaard splittings