论文标题
一对紧凑的精确拉格朗日人的条形码在刺破的精确二维符号歧管中
Barcode of a pair of compact exact Lagrangians in a punctured exact two-dimensional symplectic manifold
论文作者
论文摘要
在本文中，我们修改了一对两个紧凑的精确Lagrangian submanifolds $ l_0，l_1 $ secys symplectic 2-manifold $ m $的一对经典的浮动$ cf（l_0，l_1）$伪旋晶条通过M $中的杰出点$ h \。我们表明，该复合物在哈密顿同位素下是不变的，我们证明其条形码（如果存在）与两个条形码$ \ Mathcal {b}（cf（cf（l_0，l_1; m））$和$ \ \ \ \ \ \ m nathcal {b}（cf（l_0，l_0，l_0，l_1; m \ setmmmmmmmmmnus））n.hinus \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \这使我们能够扩展Viterbo的猜想，该猜想指出，对于$ d^* l $中的每个哈密顿同位素$ ϕ^1_h（l）$，频谱norm $γ（l，ϕ^1_h（l））$保持独立于$ h $的限制，对$ d^* l $均独立于$ h $。
In this article, we modify the classical Floer complex $CF(L_0,L_1)$ of a pair of two compact exact Lagrangian submanifolds $L_0,L_1$ of an exact symplectic 2-manifold $M$ into a $\mathbb{Z}_2[T]$-complex $CF_h(L_0,L_1)$, whose differential keeps track of how many times a pseudo-holomorphic strip passes through a distinguished point $h\in M$. We show that this complex is invariant under Hamiltonian isotopy, and we prove that its barcode, if it exists, is the same as both barcodes $\mathcal{B}(CF(L_0,L_1;M))$ and $\mathcal{B}(CF(L_0,L_1;M\setminus \{h \}))$. This allows us to extend a conjecture of Viterbo, which states that for every Hamiltonian isotopy $ϕ^1_H(L)$ in $D^* L$, the spectral norm $γ(L,ϕ^1_H(L))$ remains bounded independently of $H$, to the case of $D^* L$ with a point removed.
