Sequences of degree-one maps between geometric 3-manifolds
Sequences of degree-one maps between geometric 3-manifolds
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几何三流形之间的一阶映射序列
DOI：
10.1007/s002080050352
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
Teruhiko Soma
中科院分区：
文献类型：
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作者：
Teruhiko Soma
设M、N为闭、连通、可定向3流形。如果存在非零度映射 f: M−→ N，我们就说 N 受 M 支配。在[13]中，我们证明任何闭合的、可定向的 3-流形仅支配有限多个、可定向的、双曲 3-流形。在这里，我们考虑受控 3 流形为 Haken 的情况。任何 Haken 流形 N 都可以通过 N 中不可压缩环面的某个并唯一地分解为双曲段和 Seifert 段。我们用 H(N) 表示分解中双曲段的不相交并。如果存在受 M 支配的哈肯流形 N 并且使得 H 同胚于 H (N) 的一个分量，则称紧凑的连通 3 流形 H 被 M 作为双曲段支配。在本文中，我们将首先证明以下关于支配双曲块的有限性定理，然后给出其应用。
Let M, N be closed, connected, orientable 3-manifolds. We say that N is dominated by M if there exists a non-zero degree map f: M−→ N. In [13], we showed that any closed, orientable 3-manifold dominates only finitely many, orientable, hyperbolic 3-manifolds. Here, we consider the case when dominated 3-manifolds are Haken. Any Haken manifold N is decomposed uniquely into hyperbolic pieces and Seifert pieces by a certain union of incompressible tori in N. We denote by H (N) the disjoint union of hyperbolic pieces in the decomposition. A compact, connected 3-manifold H is said to be dominated by M as a hyperbolic piece if there exists a Haken manifold N dominated by M and such that H is homeomorphic to a component of H (N). In this paper, we will first prove the following finiteness theorem on dominated hyperbolic pieces and next give its application.