3-manifolds with planar presentations and the width of satellite knots
3-manifolds with planar presentations and the width of satellite knots
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DOI：
10.1090/s0002-9947-05-03767-0
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发表时间：
2003-04
影响因子：
1.3
通讯作者：
M. Scharlemann;J. Schultens
中科院分区：
文献类型：
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作者：
M. Scharlemann;J. Schultens
我们考虑具有浸没h到R的紧致三维流形M，其中每个通用点的逆是一个平面。S 3子流形上的标准高度函数就是一个鼓舞人心的例子。对于(M，h)，我们关联一个连通图Γ。对于M⊂S 3来说，Γ是一棵树当且仅当存在M的福克斯重嵌，它携带水平圆到互补子午线圆的完整集合。另一方面，如果S 3-M的连通图是一棵树，则存在M的保级重叠图，使得S 3-M是手柄的连通和。必然的结果。·卫星节点的宽度不小于其模式节点的宽度和so·w(K1#K2)>；max(w(K1)，w(K2))。
We consider compact 3-manifolds M having a submersion h to R in which each generic point inverse is a planar surface. The standard height function on a submanifold of S 3 is a motivating example. To (M, h) we associate a connectivity graph Γ. For M ⊂ S 3 , Γ is a tree if and only if there is a Fox reimbedding of M which carries horizontal circles to a complete collection of complementary meridian circles. On the other hand, if the connectivity graph of S 3 - M is a tree, then there is a level-preserving reimbedding of M so that S 3 - M is a connected sum of handlebodies. Corollary. • The width of a satellite knot is no less than the width of its pattern knot and so • w(K 1 #K 2 ) > max(w(K 1 ), w(K 2 )).