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2009 Stabilization, amalgamation and curves of intersection of Heegaard splittings
Ryan Derby-Talbot
Algebr. Geom. Topol. 9(2): 811-832 (2009). DOI: 10.2140/agt.2009.9.811


We address a special case of the Stabilization Problem for Heegaard splittings, establishing an upper bound on the number of stabilizations required to make a Heegaard splitting of a Haken 3–manifold isotopic to an amalgamation along an essential surface. As a consequence we show that for any positive integer n there are 3–manifolds containing an essential torus and a Heegaard splitting such that the torus and splitting surface must intersect in at least n simple closed curves. These give the first examples of lower bounds on the minimum number of curves of intersection between an essential surface and a Heegaard surface that are greater than one.


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Ryan Derby-Talbot. "Stabilization, amalgamation and curves of intersection of Heegaard splittings." Algebr. Geom. Topol. 9 (2) 811 - 832, 2009.


Received: 22 July 2008; Revised: 21 December 2008; Accepted: 18 March 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1176.57021
MathSciNet: MR2505126
Digital Object Identifier: 10.2140/agt.2009.9.811

Primary: 57M99

Rights: Copyright © 2009 Mathematical Sciences Publishers


Vol.9 • No. 2 • 2009
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