Algebraic & Geometric Topology

On non-compact Heegaard splittings

Scott A Taylor

Full-text: Open access

Abstract

A Heegaard splitting of an open 3–manifold is the partition of the manifold into two non-compact handlebodies which intersect on their common boundary. This paper proves several non-compact analogues of theorems about compact Heegaard splittings. The main result is a classification of Heegaard splittings of those open 3–manifolds obtained by removing boundary components (not all of which are 2–spheres) from a compact 3–manifold. Also studied is the relationship between exhaustions and Heegaard splittings of eventually end-irreducible 3–manifolds. It is shown that Heegaard splittings of end-irreducible 3–manifolds are formed by amalgamating Heegaard splittings of boundary-irreducible compact submanifolds.

Article information

Source
Algebr. Geom. Topol., Volume 7, Number 2 (2007), 603-672.

Dates
Received: 17 April 2006
Revised: 19 February 2007
Accepted: 16 March 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796700

Digital Object Identifier
doi:10.2140/agt.2007.7.603

Mathematical Reviews number (MathSciNet)
MR2308959

Zentralblatt MATH identifier
1134.57006

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

Keywords
non-compact 3–manifold Heegaard splitting weakly reducible

Citation

Taylor, Scott A. On non-compact Heegaard splittings. Algebr. Geom. Topol. 7 (2007), no. 2, 603--672. doi:10.2140/agt.2007.7.603. https://projecteuclid.org/euclid.agt/1513796700


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