论文标题
Legendrian Legendrian链接有限或天赋的Dynkin类型的Lagrangian填充物
Lagrangian fillings for Legendrian links of finite or affine Dynkin type
论文作者
论文摘要
我们证明，至少有许多精确的嵌入拉格朗日填充物与有限类型$ \ mathsf {ade} $的legendrian链接的种子或仿射类型$ \ tilde {\ mathsf {d}}} \ tilde {\ tilde {\ tilde {\ tilde {\ mathsf {e}} $。我们还提供旋转对称性的Lagangian填充物与$ \ Mathsf {b} $，$ \ Mathsf {g} _2 $，$ \ tilde {\ Mathsf {g}} _ 2 $，$ \ tilde { $ \ tilde {\ MathSf {C}} _ 2 $，并以偶联对称为$ \ m \ m athsf {f} _4 $，$ \ MATHSF {C} $，$ \ MATHSF {c} $，$ \ MATHSF {E} $ \ mathsf {a} _5^{（2）} $。这些家族是（无限多）精确的拉格朗日填充物（具有对称性）的第一个已知的Legendrian链接，该链接耗尽了相应的群集结构中的所有种子，超出了类型$ \ Mathsf {a} \ Mathsf {d} $。此外，我们表明（两次）$ n $ graph实现了$ \ tilde {\ mathsf {d}}} \ tilde {\ mathsf {e}} $的类型coxeter突变。尤其是，类型$ \ tilde {\ mathsf {d}} $的循环与casals和ng所考虑的循环相吻合。
We prove that there are at least as many exact embedded Lagrangian fillings as seeds for Legendrian links of finite type $\mathsf{ADE}$ or affine type $\tilde{\mathsf{D}} \tilde{\mathsf{E}}$. We also provide as many Lagrangian fillings with rotational symmetry as seeds of type $\mathsf{B}$, $\mathsf{G}_2$, $\tilde{\mathsf{G}}_2$, $\tilde{\mathsf{B}}$, or $\tilde{\mathsf{C}}_2$, and with conjugation symmetry as seeds of type $\mathsf{F}_4$, $\mathsf{C}$, $\mathsf{E}_6^{(2)}$, $\tilde{\mathsf{F}}_4$, or $\mathsf{A}_5^{(2)}$. These families are the first known Legendrian links with (infinitely many) exact Lagrangian fillings (with symmetry) that exhaust all seeds in the corresponding cluster structures beyond type $\mathsf{A} \mathsf{D}$. Furthermore, we show that the $N$-graph realization of (twice of) Coxeter mutation of type $\tilde{\mathsf{D}} \tilde{\mathsf{E}}$ corresponds to a Legendrian loop of the corresponding Legendrian links. Especially, the loop of type $\tilde{\mathsf{D}}$ coincides with the one considered by Casals and Ng.
