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Degeneration of Heegaard genus, a survey
David Bachman and Ryan Derby-Talbot
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Geometry & Topology Monographs 12
(2007) 1–15
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Abstract
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We survey known (and unknown) results about the behavior of Heegaard genus of
3-manifolds constructed via various gluings. The constructions we consider
are (1) gluing together two 3-manifolds with incompressible boundary, (2)
gluing together the boundary components of surface×I, and (3) gluing a
handlebody to the boundary of a 3-manifold. We detail those cases in which
it is known when the Heegaard genus is less than what is expected after
gluing.
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Keywords
Heegaard splitting, incompressible
surface
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Mathematical Subject Classification
Primary: 57M99, 57N10
Secondary: 57M27
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Publication
Received: 15 June 2006
Revised: 31 January 2007
Accepted: 8 February 2007
Published: 3 December 2007
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