论文标题
某些单调托里的同型拉格朗日单曲霉
Homological Lagrangian monodromy for some monotone tori
论文作者
论文摘要
鉴于符号歧管$ x $的拉格朗日submanifold $ l $，同源的拉格朗日单莫罗莫莫罗莫（Mathcal）$ \ mathcal {h} _l $描述了hamiltonian diffemormorphists $ x $保留$ l $ l $ setwise $ l $ setwise con y $ h _ _*（l）$。当$ l $是单调拉格朗日$ n $ -torus时，我们开始对该组进行系统的研究。除其他事项外，我们在$ l $是单调的复曲纤维时完全描述$ \ Mathcal {H} _l $，在对组进行分类时取得了重大进展，而不是$ n = 2 $，并对一般$ n $做出猜想。我们的分类结果至关重要地依赖于浮子共同体环的算术特性。
Given a Lagrangian submanifold $L$ in a symplectic manifold $X$, the homological Lagrangian monodromy group $\mathcal{H}_L$ describes how Hamiltonian diffeomorphisms of $X$ preserving $L$ setwise act on $H_*(L)$. We begin a systematic study of this group when $L$ is a monotone Lagrangian $n$-torus. Among other things, we describe $\mathcal{H}_L$ completely when $L$ is a monotone toric fibre, make significant progress towards classifying the groups than can occur for $n=2$, and make a conjecture for general $n$. Our classification results rely crucially on arithmetic properties of Floer cohomology rings.
