On ∂-Reducible 3-Manifolds Which Admit Complete Surface Systems (Communications in Mathematical Research, 2019)
In the present paper, we consider a class of compact orientable 3-manifoldswith one boundary component, and suppose that the manifolds are ∂-reducible andadmit complete surface systems. One of our main results says that for a compactorientable, irreducible and ∂-reducible 3-manifold M with one boundary componentF of genus $n > 0$ which admits a complete surface system S′, if D is a collectionof pairwise disjoint compression disks for ∂M, then there exists a complete surfacesystem S for M, which is equivalent to S′, such that D is disjoint from S. We alsoobtain some properties of such 3-manifolds which can be embedded in S3.
Keywords: complete surface system; ∂-reducibility; Heegaard splitting