A finiteness result for Heegaard splittings
Yoav Moriah
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We show that for a given $3$-manifold and a given Heegaard splitting there are only finitely many
complete decomposing systems of $3g - 3$ disjoint essential disks which satisfy the double rectangle condition.
This is in contrast to the infinitely many such systems of disks which only satisfy the Casson-Gordon rectangle condition.
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