Degeneration of Heegaard genus, a survey

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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 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

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Geometric Topology, 57M99, 57N10, 57M27

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http://salesiana.dossiersoluciones.com/handle/123456789/224975

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0606383
 http://arxiv.org/abs/math/0606383
 Geom. Topol. Monogr. 12 (2007) 1-15
 doi:10.2140/gtm.2007.12.1

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arXiv