Augmentations are sheaves
Augmentations are sheaves
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增强装置是滑轮
DOI：
10.2140/gt.2020.24.2149
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发表时间：
2015
影响因子：
2
通讯作者：
E. Zaslow
中科院分区：
文献类型：
--
作者：
Lenhard L. Ng;Dan Rutherford;V. Shende;Steven Sivek;E. Zaslow
我们证明了勒让德环的Chekanov-Eliashberg代数的增广集是有单位元的A-无穷范畴的结构的基础。这与[BC]中构造的非单位范畴不同，但与它的关系就像上同调与紧支上同调的关系一样。[STZ]预言了这样一个范畴的存在，他还证明了它等价于前平面上的一类层，其奇异支撑在纽结中满足无穷大。在证明了增广范畴在x线上形成了一个层之后，我们能够通过在前平面的薄片上计算这两个范畴来证明这个猜想。特别是，我们得出结论，每一个增加来自几何。
We show that the set of augmentations of the Chekanov-Eliashberg algebra of a Legendrian link underlies the structure of a unital A-infinity category. This differs from the non-unital category constructed in [BC], but is related to it in the same way that cohomology is related to compactly supported cohomology. The existence of such a category was predicted by [STZ], who moreover conjectured its equivalence to a category of sheaves on the front plane with singular support meeting infinity in the knot. After showing that the augmentation category forms a sheaf over the x-line, we are able to prove this conjecture by calculating both categories on thin slices of the front plane. In particular, we conclude that every augmentation comes from geometry.