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2008 Connected sums of unstabilized Heegaard splittings are unstabilized
David Bachman
Geom. Topol. 12(4): 2327-2378 (2008). DOI: 10.2140/gt.2008.12.2327

Abstract

Let M1 and M2 be closed, orientable 3–manifolds. Let Hi denote a Heegaard surface in Mi. We prove that if H1#H2 comes from stabilizing a lower genus splitting of M1#M2 then one of H1 or H2 comes from stabilizing a lower genus splitting. This answers a question of C Gordon (Problem 3.91 from Kirby’s problem list). We also show that every unstabilized Heegaard splitting has a unique expression as the connected sum of Heegaard splittings of prime 3–manifolds.

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David Bachman. "Connected sums of unstabilized Heegaard splittings are unstabilized." Geom. Topol. 12 (4) 2327 - 2378, 2008. https://doi.org/10.2140/gt.2008.12.2327

Information

Received: 23 November 2004; Revised: 3 May 2005; Accepted: 25 August 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1152.57020
MathSciNet: MR2443968
Digital Object Identifier: 10.2140/gt.2008.12.2327

Subjects:
Primary: 57N10
Secondary: 57M27

Rights: Copyright © 2008 Mathematical Sciences Publishers

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