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2007 On non-compact Heegaard splittings
Scott A Taylor
Algebr. Geom. Topol. 7(2): 603-672 (2007). DOI: 10.2140/agt.2007.7.603

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.

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Scott A Taylor. "On non-compact Heegaard splittings." Algebr. Geom. Topol. 7 (2) 603 - 672, 2007. https://doi.org/10.2140/agt.2007.7.603

Information

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

zbMATH: 1134.57006
MathSciNet: MR2308959
Digital Object Identifier: 10.2140/agt.2007.7.603

Subjects:
Primary: 57N10
Secondary: 57M50

Rights: Copyright © 2007 Mathematical Sciences Publishers

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