Thin position of a pair (3-manifold, 1-submanifold)
Thin position of a pair (3-manifold, 1-submanifold)
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一对的薄位置（3-歧管，1-子歧管）
DOI：
10.2140/pjm.2001.197.301
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发表时间：
2001
影响因子：
0.6
通讯作者：
K. Shimokawa
中科院分区：
文献类型：
--
作者：
Chuichiro Hayashi;K. Shimokawa
引入紧致可定向3-流形中1-子流形的Heegaard分裂和薄多重Heegaard分裂的概念，它们是桥分解和薄位置的推广。我们证明了1-子流形T的薄多重heegard分裂也是复杂度最小的heegard分裂，或者T的外部包含一个除边界平行环外具有子向边界的本质曲面。
We introduce the notions of Heegaard splittings and thin multiple Heegaard splittings of 1-submanifolds in compact orientable 3-manifolds, which are generalizations of those of bridge decompositions and thin positions. We show that either a thin multiple Heegaard splitting of 1-submanifold T is also a Heegaard splitting with minimal complexity or the exterior of T contains an essential surface with meridional boundary other than the boundary parallel annulus.