Degeneration of Heegaard genus, a survey
arXiv:math/0606383 · doi:10.2140/gtm.2007.12.1
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.
This is the version published by Geometry & Topology Monographs on 3 December 2007