Loose Legendrian embeddings in high dimensional contact manifolds
Loose Legendrian embeddings in high dimensional contact manifolds
复制标题
高维接触流形中的松散勒让德嵌入
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Emmy Murphy
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文献类型：
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作者：
Emmy Murphy
我们给出了一类至少维为$5$的接触流形上的Legendrian嵌入的$h$--主型结果。这些被称为松散的传奇，具有平凡的伪全纯不变量。我们证明，它们通过配备几乎复杂的框架的光滑同位素类而被归类为传奇同位素。这个结果本质上是高维的：维度$3$中的类似结果是错误的。
We give an $h$--principle type result for a class of Legendrian embeddings in contact manifolds of dimension at least $5$. These Legendrians, referred to as loose, have trivial pseudo-holomorphic invariants. We demonstrate they are classified up to Legendrian isotopy by their smooth isotopy class equipped with an almost complex framing. This result is inherently high dimensional: analogous results in dimension $3$ are false.