Geometry & Topology

Connected sums of unstabilized Heegaard splittings are unstabilized

David Bachman

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57M27: Invariants of knots and 3-manifolds

Heegaard splitting connected sum incompressible surface


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.

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