Geometry & Topology

Heegaard surfaces and the distance of amalgamation

Tao Li

Full-text: Open access

Abstract

Let M1 and M2 be orientable irreducible 3–manifolds with connected boundary and suppose M1M2. Let M be a closed 3–manifold obtained by gluing M1 to M2 along the boundary. We show that if the gluing homeomorphism is sufficiently complicated, then M is not homeomorphic to S3 and all small-genus Heegaard splittings of M are standard in a certain sense. In particular, g(M)=g(M1)+g(M2)g(Mi), where g(M) denotes the Heegaard genus of M. This theorem is also true for certain manifolds with multiple boundary components.

Article information

Source
Geom. Topol., Volume 14, Number 4 (2010), 1871-1919.

Dates
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
https://projecteuclid.org/euclid.gt/1513883509

Digital Object Identifier
doi:10.2140/gt.2010.14.1871

Mathematical Reviews number (MathSciNet)
MR2680206

Zentralblatt MATH identifier
1207.57031

Subjects
Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57M50: Geometric structures on low-dimensional manifolds

Keywords
Heegaard splitting amalgamation curve complex

Citation

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


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