Stable functions and common stabilizations of Heegaard splittings

Johnson, Jesse

doi:10.1090/S0002-9947-09-04731-X

Stable functions and common stabilizations of Heegaard splittings
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Trans. Amer. Math. Soc. 361 (2009), 3747-3765 Request permission

Abstract:

We present a new proof of Reidemeister and Singer’s Theorem that any two Heegaard splittings of the same 3-manifold have a common stabilization. The proof leads to an upper bound on the minimal genus of a common stabilization in terms of the number of negative slope inflection points and type two cusps in a Rubinstein-Scharlemann graphic for the two splittings.

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