树奇异性和松散的Legendrians
Arboreal singularities and loose Legendrians I
摘要：
树奇异点是拉格朗日奇异点的一个重要类别。它们是圆锥形的，这意味着可以通过研究它们的联系来理解它们，这些联系是$S^{2n-1}_{\text{std}}$中的奇异勒让德空间。松勒让德空间是一类满足$h$ -原理的勒让德空间，这意味着它们的几何分类与它们的拓扑型是双射对应的。对于特殊情况下的线性树奇异性，我们表明，构造层足以检测是否有任何闭集的树链接是松散的。
英文摘要：
Arboreal singularities are an important class of Lagrangian singularities. They are conical, meaning that they can be understood by studying their links, which are singular Legendrian spaces in $S^{2n-1}_{\text{std}}$. Loose Legendrians are a class of Legendrian spaces which satisfy an $h$--principle, meaning that their geometric classification is in bijective correspondence with their topological types. For the particular case of the linear arboreal singularities, we show that constructable sheaves suffice to detect whether any closed set of an arboreal link is loose.
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