Comparing Heegaard and JSJ structures of orientable 3-manifolds
Comparing Heegaard and JSJ structures of orientable 3-manifolds
复制标题
可定向 3 流形的 Heegaard 和 JSJ 结构比较
DOI：
10.1090/s0002-9947-00-02654-4
复制
发表时间：
1998
影响因子：
1.3
通讯作者：
J. Schultens
中科院分区：
文献类型：
--
作者：
M. Scharlemann;J. Schultens
不可约闭可定向3-流形的Heegaard亏格g限制了流形通过其标准环面的E-Shalen-Johannson分解中出现的块的数量和复杂性。例如，如果p个互补分量不是塞弗特纤维，则p ≤ g − 1。这概括了小林的工作。Heegaard亏格g也对塞弗特块的复杂性给出了明确的界限。例如，如果塞弗特片的并有基空间P和f个例外纤维，则f − χ（P）≤ 3g − 3− p。
The Heegaard genus g of an irreducible closed orientable 3-manifold puts a limit on the number and complexity of the pieces that arise in the Jaco-Shalen-Johannson decomposition of the manifold by its canonical tori. For example, if p of the complementary components are not Seifert fibered, then p ≤ g − 1. This generalizes work of Kobayashi. The Heegaard genus g also puts explicit bounds on the complexity of the Seifert pieces. For example, if the union of the Seifert pieces has base space P and f exceptional fibers, then f − χ(P ) ≤ 3g − 3− p.