Abstract We give a computation of the Legendrian contact homology (LCH) DGA for an arbitrary generic Legendrian surface L in the 1-jet space of a surface. As input we require a suitable cellular decomposition of the base projection of L. A collection of generators is associated to each cell, and the differential is given by explicit matrix formulas. In the present article, we prove that the equivalence class of this cellular DGA does not depend on the choice of decomposition, and in the sequel papers [35] , [36] we use this result to show that the cellular DGA is equivalent to the usual Legendrian contact homology DGA defined via holomorphic curves. Extensions are made to allow Legendrians with non-generic cone-point singularities. We apply our approach to compute the LCH DGA for several examples including an infinite family, and to give general formulas for DGAs of front spinnings allowing for the axis of symmetry to intersect L.

中文翻译：

---

表面的细胞 Legendrian 接触同源性，第 I 部分

摘要 我们计算了表面的 1 射流空间中任意通用勒让德表面 L 的勒让德接触同调 (LCH) DGA。作为输入，我们需要对 L 的基本投影进行适当的元胞分解。生成器的集合与每个元胞相关联，并且微分由显式矩阵公式给出。在本文中，我们证明了这种细胞 DGA 的等价类不依赖于分解的选择，并且在后续论文 [35]、[36] 中，我们使用这个结果来证明细胞 DGA 等价于通过全纯曲线定义的通常的勒让德接触同源 DGA。进行扩展以允许具有非通用锥点奇点的 Legendrians。我们应用我们的方法来计算 LCH DGA 的几个例子，包括无限族，