Given an augmentation for a Legendrian surface in a 1-jet space, \(\Lambda \subset J^1(M)\), we explicitly construct an object, \(\mathcal {F} \in \mathbf {Sh}^\bullet _{\Lambda }(M\times \mathbb {R}, \mathbb {K})\), of the (derived) category from Viterbo (Shende, V., Treumann, D., Zaslow, E. Invent Math 207(3), 1031–1133 (2017)) of constructible sheaves on \(M\times \mathbb {R}\) with singular support determined by \(\Lambda \). In the construction, we introduce a simplicial Legendrian DGA (differential graded algebra) for Legendrian submanifolds in 1-jet spaces that, based on Rutherford and Sullivan (Cellular Legendrian contact homology for surfaces, Part I, arXiv:1608.02984.) Rutherford and Sullivan (Internat J Math 30(7):135, 2019) Rutherford and Sullivan (Internat J Math 30(7):111, 2019), is equivalent to the Legendrian contact homology DGA in the case of Legendrian surfaces. In addition, we extend the approach of Viterbo (Shende, V., Treumann, D., Zaslow, E. Invent Math 207(3), 1031–1133 (2017)) for 1-dimensional Legendrian knots to obtain a combinatorial model for sheaves in \(\mathbf {Sh}^\bullet _{\Lambda }(M\times \mathbb {R}, \mathbb {K})\) in the 2-dimensional case.

给定 1-jet 空间中 Legendrian 曲面的增强\(\Lambda \subset J^1(M)\)，我们明确构造一个对象\(\mathcal {F} \in \mathbf {Sh}^ \bullet _{\Lambda }(M\times \mathbb {R}, \mathbb {K})\)，来自 Viterbo (Shende, V., Treumann, D., Zaslow, E. Invent) 的（派生）类别数学207 (3), 1031–1133 (2017)) 在\(M\times \mathbb {R}\)上的可构造滑轮，具有由\(\Lambda \)确定的奇异支持. 在构造中，我们为 1-jet 空间中的 Legendrian 子流形引入了一个简单的 Legendrian DGA（微分梯度代数），它基于 Rutherford 和 Sullivan（表面的 Cellular Legendrian 接触同源性，第一部分，arXiv：1608.02984。）Rutherford 和 Sullivan（ Internat J Math 30(7):135, 2019) Rutherford and Sullivan (Internat J Math 30(7):111, 2019)，在 Legendrian 曲面的情况下等效于 Legendrian 接触同源 DGA。此外，我们扩展了 Viterbo (Shende, V., Treumann, D., Zaslow, E. Invent Math 207 (3), 1031–1133 (2017)) 用于一维勒让德里亚结的方法以获得组合模型在二维情况下\(\mathbf {Sh}^\bullet _{\Lambda }(M\times \mathbb {R}, \mathbb {K})\)中的滑轮。