Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 7, Number 2 (2007), 1119-1134.
Saddle tangencies and the distance of Heegaard splittings
We give another proof of a theorem of Scharlemann and Tomova and of a theorem of Hartshorn. The two theorems together say the following. Let be a compact orientable irreducible 3–manifold and a Heegaard surface of . Suppose is either an incompressible surface or a strongly irreducible Heegaard surface in . Then either the Hempel distance or is isotopic to . This theorem can be naturally extended to bicompressible but weakly incompressible surfaces.
Algebr. Geom. Topol., Volume 7, Number 2 (2007), 1119-1134.
Received: 7 January 2007
Revised: 1 June 2007
Accepted: 25 July 2007
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: 57M50: Geometric structures on low-dimensional manifolds
Li, Tao. Saddle tangencies and the distance of Heegaard splittings. Algebr. Geom. Topol. 7 (2007), no. 2, 1119--1134. doi:10.2140/agt.2007.7.1119. https://projecteuclid.org/euclid.agt/1513796717