论文标题
模棱两可的符号同源性，线性接触同源性和拉格朗日能力
Equivariant symplectic homology, linearized contact homology and the Lagrangian capacity
论文作者
论文摘要
我们从“ Cieliebak and Mohnke-刺穿的全态曲线和Lagrangian嵌入”中建立了有关拉格朗日能力的计算结果。更确切地说，我们表明，4维凸圆形域的拉格朗日能力等于其对角线。证明涉及比较Lagrangian的能力，“ McDuff和Siegel的McDuff-Siegel能力 - 符号能力 - 符号能力，无扰动的曲线和凸出的圆环域”以及来自“ Gutt-Hutchings的能力”，来自” Gutt和Hutchings and Hutchings-smplectic-symplectic sompecties sompectempemplectimplecticaliant simptecticaliant simpticaliant simpticaliant simpticaliant''。在假设有一个合适的虚拟扰动方案的假设下工作，该方案定义了线性化接触同源性的曲线计数，我们将先前的结果扩展到凸或凹形和任何维度的复曲面域。为此，我们使用“ Siegel-较高的符号能力”的较高符号能力。关键步骤是表明椭圆形中渐近圆柱形圆形曲线的模量空间横向切除。
We establish computational results concerning the Lagrangian capacity from "Cieliebak and Mohnke - Punctured holomorphic curves and Lagrangian embeddings". More precisely, we show that the Lagrangian capacity of a 4-dimensional convex toric domain is equal to its diagonal. The proof involves comparisons between the Lagrangian capacity, the McDuff-Siegel capacities from "McDuff and Siegel - Symplectic capacities, unperturbed curves, and convex toric domains", and the Gutt-Hutchings capacities from "Gutt and Hutchings - Symplectic capacities from positive S1-equivariant symplectic homology". Working under the assumption that there is a suitable virtual perturbation scheme which defines the curve counts of linearized contact homology, we extend the previous result to toric domains which are convex or concave and of any dimension. For this, we use the higher symplectic capacities from "Siegel - Higher symplectic capacities". The key step is showing that moduli spaces of asymptotically cylindrical holomorphic curves in ellipsoids are transversely cut out.
