Geometry & Topology
- Geom. Topol.
- Volume 12, Number 4 (2008), 2327-2378.
Connected sums of unstabilized Heegaard splittings are unstabilized
Let and be closed, orientable 3–manifolds. Let denote a Heegaard surface in . We prove that if comes from stabilizing a lower genus splitting of then one of or 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.
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
Permanent link to this document
Digital Object Identifier
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
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