论文标题
在Lagrangians的最小符号区域
On the minimal symplectic area of Lagrangians
论文作者
论文摘要
我们表明，拉格朗日亚策略的最小象征区域在符合性的非球面域中普遍界定，并具有消失的符号共同体学。如果确切的域名允许$ k $ -semi污染，那么最小的符号区域通常以$ k（π，1）$ lagrangians为界。作为推论，我们表明Arnol'd Chord的猜想在以下四种情况下保存：（1）$ y $允许使用$ SH^*（w）= 0 $（对于某些环系数）; （2）$ y $在$ sh^*（w）= 0 $和简单地连接的legendrians上符合符合性的非球形填充； （3）$ y $承认了一个$ k $ -semi-dialation的精确填充，而legendrian为$ k（π，1）$ space; （4）$ y $是cosphere束$ s^*q $，$π_2（q）\ to H_2（q）$ nontivial，Legendrian具有微不足道的$π_2$。此外，在情况（1）的情况下，我们获得了同质轨道的存在。我们还提供了更多的示例，其中包括$ k $ -semi-dimentations $ \ ge 4 $。
We show that the minimal symplectic area of Lagrangian submanifolds are universally bounded in symplectically aspherical domains with vanishing symplectic cohomology. If an exact domain admits a $k$-semi-dilation, then the minimal symplectic area is universally bounded for $K(π,1)$-Lagrangians. As a corollary, we show that Arnol'd chord conjecture holds for the following four cases: (1) $Y$ admits an exact filling with $SH^*(W)=0$ (for some ring coefficient); (2) $Y$ admits a symplectically aspherical filling with $SH^*(W)=0$ and simply connected Legendrians; (3) $Y$ admits an exact filling with a $k$-semi-dilation and the Legendrian is a $K(π,1)$ space; (4) $Y$ is the cosphere bundle $S^*Q$ with $π_2(Q)\to H_2(Q)$ nontrivial and the Legendrian has trivial $π_2$. In addition, we obtain the existence of homoclinic orbits in case (1). We also provide many more examples with $k$-semi-dilations in all dimensions $\ge 4$.
