论文标题
通过全球维度功能的稳定条件的收缩流
Contractible flow of stability conditions via global dimension function
论文作者
论文摘要
我们介绍了一种分析方法，该方法使用全局尺寸函数$ \ operatorname {gldim} $在空间上产生可缩度流，以$ \ operatatorName {stab} \ Mathcal {d} $稳定条件的稳定性条件上的三角形类别$ \ nathcal {d} $。在$ \ Mathcal {d} = \ Mathcal {d}（\ Mathbf {s}^λ）$的情况下，是分级表面$ \ Mathbf {s}^λ$的拓扑fukaya类别$ \ operatorName {gldim}^{ - 1}（0，x）$对于任何$ 1 \ le x \ le y $，提供$（x，y）$不包含'critical'值$ \ \ \ \ {1+w_ \ partial/m_ \ partial/m_ \ partial/m_ \ partial \ partial \ partial \ partial \ partial \ pot \ partial \ in \ partial \ mathbf {s}^λ\} $，其中一对$（m_ \ partial，w_ \ partial）$由数字$ $ m_ \分标点的部分$组成，绕线$ w_ \ partial $ w_ \ partial $ w_ \ partial $与边界组成$ \ partial $ \ partial $ of $ \ partial $ of $ \ $ \ $ \ $ \ $ \ $ \ s.s结果是，$ \ Mathcal {d}（\ Mathbf {s}^λ）$的全局维度必须是这些关键值之一。 此外，我们删除了kikuta-ouchi-takahashi分类的假设结果，其三角形类别的全球维度小于1。
We introduce an analytic method that uses the global dimension function $\operatorname{gldim}$ to produce contractible flows on the space $\operatorname{Stab}\mathcal{D}$ of stability conditions on a triangulated category $\mathcal{D}$. In the case when $\mathcal{D}=\mathcal{D}(\mathbf{S}^λ)$ is the topological Fukaya category of a graded surface $\mathbf{S}^λ$, we show that $\operatorname{gldim}^{-1}(0,y)$ contracts to $\operatorname{gldim}^{-1}(0,x)$ for any $1\le x\le y$, provided $(x,y)$ does not contain `critical' values $\{1+w_\partial/m_\partial \mid w_\partial\ge0, \partial\in\partial\mathbf{S}^λ\}$, where the pair $(m_\partial,w_\partial)$ consists of the number $m_\partial$ of marked points and the winding number $w_\partial$ associated to a boundary component $\partial$ of $\mathbf{S}^λ$. One consequence is that the global dimension of $\mathcal{D}(\mathbf{S}^λ)$ must be one of these critical values. Besides, we remove the assumptions in Kikuta-Ouchi-Takahashi's classification result on triangulated categories with global dimension less than 1.
