On -reducible 3-manifolds Which Admit Complete Surface Systems

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 > 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 S3.

在本文中，我们考虑一类具有一个边界分支的紧致可定向3 - 流形，并假设这些流形是@ - 可约的且允许完备曲面系。我们的一个主要结果表明：对于一个具有一个亏格\(n>0\)的边界分支\(F\)的紧致可定向、不可约且@ - 可约的3 - 流形\(M\)，若它允许一个完备曲面系\(S′\)，如果\(D\)是一组两两不相交的\(\partial M\)的压缩圆盘，那么存在一个\(M\)的完备曲面系\(S\)，它与\(S′\)等价，使得\(D\)与\(S\)不相交。我们还得到了这类可嵌入\(S^3\)的3 - 流形的一些性质。 注：其中“@ - 可约”这种表述可能是特定数学领域中的专业术语，可能有更准确的中文翻译，如果有相关背景知识补充，翻译会更准确。