论文标题
单调的Lagrangians在cotangent束的球形捆绑包中
Monotone Lagrangians in cotangent bundles of spheres
论文作者
论文摘要
我们研究$ t^*s^n $的紧凑型单调福卡亚类别，以$ n \ geq 2 $，并表明它是由两个类别的对象分配的：零部分$ s^n $（配备了合适的边界小心），并与单调的lagrangian lagrangian lagrangian lagrangian lagrangian lagrangian loghangangian tori $（常数$τ> 0 $（配备了等级1统一本地系统）。结果，任何可从$ s^n $或$（s^1 \ times s^{n-1}）中的任何可封闭的可定向旋转单调拉格朗日（可能配备了辅助数据）都是不可替代的。在$ t^*s^3 $的情况下，单调lagrangians $（s^1 \ times s^2）_τ$可以由单调tori $ t^3_τ$的家族代替。
We study the compact monotone Fukaya category of $T^*S^n$, for $n\geq 2$, and show that it is split-generated by two classes of objects: the zero-section $S^n$ (equipped with suitable bounding cochains) and a 1-parameter family of monotone Lagrangian tori $(S^1\times S^{n-1})_τ$, with monotonicity constants $τ>0$ (equipped with rank 1 unitary local systems). As a consequence, any closed orientable spin monotone Lagrangian (possibly equipped with auxiliary data) with non-trivial Floer cohomology is non-displaceable from either $S^n$ or one of the $(S^1\times S^{n-1})_τ$. In the case of $T^*S^3$, the monotone Lagrangians $(S^1\times S^2)_τ$ can be replaced by a family of monotone tori $T^3_τ$.
