We show that Scharlemann-Thompson untelescoping of Heegaard splittings is finer than Casson-Gordon's by giving concrete examples.
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The paper shows how to transform certain 3-manifold Heegaard splittings into simpler forms.
problem Weakly reducible Heegaard splittings with limited compression disks.
method Untelescoping of Heegaard splittings to simplify structures.
result Transformed splittings have fewer compression disks and clearer structures.
Let be a graph in a compact, orientable 3--manifold and let be a subgraph. can be placed in bridge position with respect to a Heegaard surface . We show that if is what we call -c-weakly reducible in the complement of then either a "degenerate" situation occurs or can be untelescop…