HIGH DISTANCE KNOTS IN CLOSED 3-MANIFOLDS
HIGH DISTANCE KNOTS IN CLOSED 3-MANIFOLDS
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DOI：
10.1142/s0218216511009637
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发表时间：
2009-11
影响因子：
0.5
通讯作者：
Marion Campisi;M. Rathbun
中科院分区：
文献类型：
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作者：
Marion Campisi;M. Rathbun
设M是具有给定Heegaard分裂的闭三维流形。我们表明，在一个单一的稳定，一些稳定的分裂核有任意高的距离分裂面。这推广了Minsky、Moriah和Schleimer关于S3中纽结的结果。我们还表明，在复杂的曲线中，手柄体集要么粗略不同，要么相同。定义了Heegaard分裂的粗映射类群，并证明了如果（S，V，W）是亏格≥2的Heegaard分裂，则（S，V，W）的粗映射类群与（S，V，W）的映射类群同构.
Let M be a closed 3-manifold with a given Heegaard splitting. We show that after a single stabilization, some core of the stabilized splitting has arbitrarily high distance with respect to the splitting surface. This generalizes a result of Minsky, Moriah, and Schleimer for knots in S3. We also show that in the complex of curves, handlebody sets are either coarsely distinct or identical. We define the coarse mapping class group of a Heegaard splitting, and show that if (S, V, W) is a Heegaard splitting of genus ≥2, then the coarse mapping class group of (S, V, W) is isomorphic to the mapping class group of (S, V, W).