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On the Heegaard splittings of amalgamated 3–manifolds

Tao Li

Geometry & Topology Monographs 12 (2007) 157–190

DOI: 10.2140/gtm.2007.12.157

arXiv: math.GT/0701395

Abstract
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We give a combinatorial proof of a theorem first proved by Souto which says the following. Let M1 and M2 be simple 3–manifolds with connected boundary of genus g>0. If M1 and M2 are glued via a complicated map, then every minimal Heegaard splitting of the resulting closed 3–manifold is an amalgamation. This proof also provides an algorithm to find a bound on the complexity of the gluing map.

Keywords

Heegaard splitting, amalgamation, curve complex, sample layout

Mathematical Subject Classification

Primary: 57N10

Secondary: 57M50

References
Publication

Received: 19 November 2006
Revised: 31 August 2007
Accepted: 18 September 2007
Published: 3 December 2007

Authors
Tao Li
Department of Mathematics
Boston College
Chestnut Hill, MA 02467
USA
http://www2.bc.edu/~taoli