TY - JOUR
T1 - On ∂-Reducible 3-Manifolds Which Admit Complete Surface Systems
AU - Zhao , Yan
AU - Lei , Fengchun
AU - Li , Fengling
JO - Communications in Mathematical Research 
VL - 3
SP - 215
EP - 222
PY - 2019
DA - 2019/11
SN - 33
DO - http://doi.org/10.13447/j.1674-5647.2017.03.03
UR - https://global-sci.org/intro/article_detail/cmr/13377.html
KW - complete surface system, ∂-reducibility, Heegaard splitting
AB - <p style="text-align: justify;">In the present paper, we consider a class of compact orientable 3-manifolds
with one boundary component, and suppose that the manifolds are ∂-reducible and
admit complete surface systems. One of our main results says that for a compact
orientable, irreducible and ∂-reducible 3-manifold M with one boundary component
F of genus $n &gt; 0$ which admits a complete surface system S′
, if D is a collection
of pairwise disjoint compression disks for ∂M, then there exists a complete surface
system S for M, which is equivalent to S′
, such that D is disjoint from S. We also
obtain some properties of such 3-manifolds which can be embedded in S<sup>3</sup>.</p>