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arXiv:math/0606383 [math.GT]AbstractReferencesReviewsResources

Degeneration of Heegaard genus, a survey

David Bachman, Ryan Derby-Talbot

Published 2006-06-15, updated 2009-03-30Version 4

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 times 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.

Comments: This is the version published by Geometry & Topology Monographs on 3 December 2007
Journal: Geom. Topol. Monogr. 12 (2007) 1-15
Categories: math.GT
Subjects: 57M99, 57N10, 57M27
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