Incompressible surfaces in handlebodies and boundary reducible 3-manifolds

Details Incompressible surfaces in handlebodies and boundary reducible 3-manifolds Incompressible surfaces in handlebodies and boundary reducible 3-manifolds

2009-11-01

arxiv.org/abs/0911.0207v2

Topology and its Applications Volume 158, Issue 4, 2011, Pages 551-571

Mathematics

Geometric Topology

33 pages, 14 figures

Scientific paper

10.1016/j.topol.2010.11.014

We study the existence of incompressible embeddings of surfaces into the genus two handlebody. We show that for every compact surface with boundary, orientable or not, there is an incompressible embedding of the surface into the genus two handlebody. In the orientable case the embedding can be either separating or non-separating. We also consider the case in which the genus two handlebody is replaced by an orientable 3-manifold with a compressible boundary component of genus greater than or equal to two.

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