The Heegaard Genus of Amalgamated 3Manifolds
 Marc Lackenby
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Let M and M′ be simple 3manifolds, each with connected boundary of genus at least two. Suppose that Mand M′ are glued via a homeomorphism between their boundaries. Then we show that, provided the gluing homeomorphism is ‘sufficiently complicated’, the Heegaard genus of the amalgamated manifold is completely determined by the Heegaard genus of Mand M′ and the genus of their common boundary. Here, a homeomorphism is ‘sufficiently complicated’ if it is the composition of a homeomorphism from the boundary ofM to some surface S, followed by a sufficiently high power of a pseudoAnosov onS, followed by a homeomorphism to the boundary of M′. The proof uses the hyperbolic geometry of the amalgamated manifold, generalised Heegaard splittings and minimal surfaces.
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 Title
 The Heegaard Genus of Amalgamated 3Manifolds
 Journal

Geometriae Dedicata
Volume 109, Issue 1 , pp 139145
 Cover Date
 20041201
 DOI
 10.1007/s107110046553y
 Print ISSN
 00465755
 Online ISSN
 15729168
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 3manifold
 Heegaard genus
 Haken manifold
 minimal surfaces
 hyperbolic geometry
 Industry Sectors
 Authors

 Marc Lackenby ^{(1)}
 Author Affiliations

 1. Mathematical Institute, Oxford University, 24–29 St Giles’, Oxford, OX1 3LB, United Kingdom