论文标题
真实的拉格朗日摩托车和价值变形
Real Lagrangian Tori and Versal Deformations
论文作者
论文摘要
给定的Lagrangian submanifold是否可以将其视为反隔离相关性的固定点集？如果是这样，则称为\ emph {real}。在附近的拉格朗日人的流离失所方面，我们妨碍了封闭的拉格朗日亚曼菲尔德的封闭式submanifold。将这种障碍物应用于复曲面纤维，我们获得了许多（甚至所有）曲圈单调式歧管的中心纤维，只有当相应的矩多层中心对称时，才是真实的。此外，我们将Chekanov圆环嵌入了所有感谢您的单调象征歧管中，并表明它是异国情调的，不是真实的，以$ S^2 \ times s^2 $扩展了Kim的结果（Arxiv：1909.09972）。在$ s^2 $的产品中，我们表明Chekanov Tori的所有产品都是成对的，也不是真实的。这些结果表明，真正的托里很少见。我们的方法是基本的，因为我们不使用〜$ j $ - 摩尔形曲线。取而代之的是，我们依赖于$ \ mathbb {r}^{2n} $中的symplectic降低和product tori的位移能量。
Can a given Lagrangian submanifold be realized as the fixed point set of an anti-symplectic involution? If so, it is called \emph{real}. We give an obstruction for a closed Lagrangian submanifold to be real in terms of the displacement energy of nearby Lagrangians. Applying this obstruction to toric fibres, we obtain that the central fibre of many (and probably all) toric monotone symplectic manifolds is real only if the corresponding moment polytope is centrally symmetric. Furthermore, we embed the Chekanov torus in all toric monotone symplectic manifolds and show that it is exotic and not real, extending Kim's result (arXiv:1909.09972) for $S^2 \times S^2$. Inside products of $S^2$, we show that all products of Chekanov tori are pairwise distinct and not real either. These results indicate that real tori are rare. Our methods are elementary in the sense that we do not use~$J$-holomorphic curves. Instead, we rely on symplectic reduction and the displacement energy of product tori in $\mathbb{R}^{2n}$.
