Degeneration of Heegaard genus, a survey

Details Degeneration of Heegaard genus, a survey Degeneration of Heegaard genus, a survey

2006-06-15

arxiv.org/abs/math/0606383v4

Geom. Topol. Monogr. 12 (2007) 1-15

Mathematics

Geometric Topology

This is the version published by Geometry & Topology Monographs on 3 December 2007

Scientific paper

10.2140/gtm.2007.12.1

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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