Volume 7, issue 2 (2007)

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On non-compact Heegaard splittings

Scott A Taylor

Algebraic & Geometric Topology 7 (2007) 603–672

arXiv: math.GT/0602581

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.

Keywords
non-compact 3–manifold, Heegaard splitting, weakly reducible
Mathematical Subject Classification 2000
Primary: 57N10
Secondary: 57M50
References
Publication
Received: 17 April 2006
Revised: 19 February 2007
Accepted: 16 March 2007
Published: 10 May 2007
Authors
Scott A Taylor
Mathematics Department
University of California
Santa Barbara, CA 93101
USA