Augmentations and rulings of Legendrian knots
Augmentations and rulings of Legendrian knots
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传奇结的增强和裁决
DOI：
10.1155/imrn.2005.1157
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发表时间：
2004
影响因子：
1
通讯作者：
J. Sabloff
中科院分区：
文献类型：
--
作者：
J. Sabloff
建立了Legendrian节的全纯族不变量与生成族不变量之间的联系；即，一个Legendrian结的判定（或分解）的存在性等价于它的接触同调的增广的存在性。这个结果是Fuchs和Ishkhanov用不同的方法独立得到的。对该证明的仔细研究得出了一种构造给定增广的规则的算法。最后，得到了关于旋转数的增广存在的条件。
A connection between holomorphic and generating family invariants of Legendrian knots is established; namely, that the existence of a ruling (or decomposition) of a Legendrian knot is equivalent to the existence of an augmentation of its contact homology. This result was obtained independently and using different methods by Fuchs and Ishkhanov [12]. Close examination of the proof yields an algorithm for constructing a ruling given an augmentation. Finally, a condition for the existence of an augmentation in terms of the rotation number is obtained.