可分解精确拉格朗日填充的一个障碍
An obstruction to decomposable exact Lagrangian fillings
摘要：
研究了具有标准切触结构的$\mathbb{R}^3$中Legendrian链之间的可分解精确拉格朗日配边的性质.特别地，对于勒让德链$K$的任何可分解精确拉格朗日填充$L$，我们可以获得与$L$相关联的$K$的正规规则。我们证明了相应的正规定则必须有偶数个钩环。因此，我们给出了一个特殊的Legendrian $(4,-(2n+5))$ -环面结，对于每个$n \geq 0$，它没有可分解的精确拉格朗日填充，因为它只有1个正常的规则，这个正常的规则有奇数的扣。
英文摘要：
We study some properties of decomposable exact Lagrangian cobordisms between Legendrian links in $\mathbb{R}^3$ with the standard contact structure. In particular, for any decomposable exact Lagrangian filling $L$ of a Legendrian link $K$, we may obtain a normal ruling of $K$ associated with $L$. We prove that the associated normal rulings must have even number of clasps. As a result, we give a particular Legendrian $(4,-(2n+5))$-torus knot, for each $n \geq 0$, which does not have a decomposable exact Lagrangian filling because it has only 1 normal ruling and this normal ruling has odd number of clasps.
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