Geometry & Topology 12 (2008) 2327–2378

DOI: 10.2140/gt.2008.12.2327

Abstract

Let M₁ and M₂ be closed, orientable 3–manifolds. Let H_i denote a Heegaard surface in M_i. 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.

Keywords

Heegaard splitting, connected sum, incompressible surface

Mathematical Subject Classification

Primary: 57N10

Secondary: 57M27

References

Publication

Received: 23 November 2004
Revised: 3 May 2005
Accepted: 25 August 2008
Published: 15 September 2008
Proposed: David Gabai
Seconded: Colin Rourke, Joan Birman

Authors