Anosov flows on Dehn surgeries on the figure-eight knot
Anosov flows on Dehn surgeries on the figure-eight knot
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阿诺索夫在德恩的八字结手术上流淌
DOI：
10.1215/00127094-2022-0079
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发表时间：
2021
影响因子：
2.5
通讯作者：
B. Yu
中科院分区：
文献类型：
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作者：
B. Yu
本文的目的是对由Dehn手术在8字形结上得到的3流形上的Anosov流进行分类。这组3-流形用M(r)表示（r是一个比例数），它包含了古德曼发现的历史上第一类允许Anosov流的双曲型3-流形。结合Plante对土壤流形M(0)上的Anosov流的分类，我们得到：1。如果r是整数，在拓扑等价的情况下，M(r)精确携带一个唯一的Anosov流，该Anosov流由Goodman通过对悬浮Anosov流进行Dehn-Fried-Goodman手术构造；2. 如果r不是整数，则M(r)不携带任何Anosov流。作为第二个结果的结果，我们得到了无限多个带紧叶但不带任何Anosov流的闭合可定向双曲3-流形。证明中的基本工具是Schwider构建的分支曲面集，它用于携带M(r)上的基本层合。
The purpose of this paper is to classify Anosov flows on the 3-manifolds obtained by Dehn surgeries on the figure-eight knot. This set of 3-manifolds is denoted by M(r) (r is a ratioanl number), which contains the first class of hyperbolic 3-manifolds admitting Anosov flows in history, discovered by Goodman. Combining with the classification of Anosov flows on the sol-manifold M(0) due to Plante, we have: 1. if r is an integer, up to topological equivalence, M(r) exactly carries a unique Anosov flow, which is constructed by Goodman by doing a Dehn-Fried-Goodman surgery on a suspension Anosov flow; 2. if r is not an integer, M(r) does not carry any Anosov flow. As a consequence of the second result, we get infinitely many closed orientable hyperbolic 3-manifolds which carry taut foliations but does not carry any Anosov flow. The fundamental tool in the proofs is the set of branched surfaces built by Schwider, which is used to carry essential laminations on M(r).
DOI：
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发表时间：
2009
期刊：
影响因子：
--
作者：
小林毅;村井紘子;村井紘子;H. Murai
通讯作者：
H. Murai