Comparing Heegaard splittings -the bounded case

Rubinstein, Hyam; Scharlemann, Martin

doi:10.1090/S0002-9947-98-01824-8

Comparing Heegaard splittings -the bounded case
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by Hyam Rubinstein and Martin Scharlemann PDF

Trans. Amer. Math. Soc. 350 (1998), 689-715 Request permission

Abstract:

In a recent paper we used Cerf theory to compare strongly irreducible Heegaard splittings of the same closed irreducible orientable 3-manifold. This captures all irreducible splittings of non-Haken 3-manifolds. One application is a solution to the stabilization problem for such splittings: If $p \leq q$ are the genera of two splittings, then there is a common stabilization of genus $5p + 8q - 9$. Here we show how to obtain similar results even when the 3-manifold has boundary.

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