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Degeneration of Heegaard genus, a survey

David Bachman·Ryan Derby-Talbot
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Abstract

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.

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David Bachman, Ryan Derby-Talbot. 2009-03-30. Degeneration of Heegaard genus, a survey. https://doi.org/10.2140/gtm.2007.12.1

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