Geometry & Topology

Connected sums of unstabilized Heegaard splittings are unstabilized

David Bachman

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.

Article information

Source
Geom. Topol., Volume 12, Number 4 (2008), 2327-2378.

Dates
Revised: 3 May 2005
Accepted: 25 August 2008
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513800128

Digital Object Identifier
doi:10.2140/gt.2008.12.2327

Mathematical Reviews number (MathSciNet)
MR2443968

Zentralblatt MATH identifier
1152.57020

Subjects
Secondary: 57M27: Invariants of knots and 3-manifolds

Citation

Bachman, David. Connected sums of unstabilized Heegaard splittings are unstabilized. Geom. Topol. 12 (2008), no. 4, 2327--2378. doi:10.2140/gt.2008.12.2327. https://projecteuclid.org/euclid.gt/1513800128

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