Geometry & Topology
- Geom. Topol.
- Volume 14, Number 4 (2010), 1871-1919.
Heegaard surfaces and the distance of amalgamation
Let and be orientable irreducible –manifolds with connected boundary and suppose . Let be a closed –manifold obtained by gluing to along the boundary. We show that if the gluing homeomorphism is sufficiently complicated, then is not homeomorphic to and all small-genus Heegaard splittings of are standard in a certain sense. In particular, , where denotes the Heegaard genus of . This theorem is also true for certain manifolds with multiple boundary components.
Geom. Topol., Volume 14, Number 4 (2010), 1871-1919.
Received: 31 July 2008
Revised: 9 March 2010
Accepted: 7 June 2010
First available in Project Euclid: 21 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. Heegaard surfaces and the distance of amalgamation. Geom. Topol. 14 (2010), no. 4, 1871--1919. doi:10.2140/gt.2010.14.1871. https://projecteuclid.org/euclid.gt/1513883509