论文标题
2参数持久模块的可分解性的本地特征
Local characterizations for decomposability of 2-parameter persistence modules
论文作者
论文摘要
我们研究了足够的当地条件的存在，在该条件下，POSET表示将其作为来自给定类别的不可分解的直接总和。在我们的工作中，索引POSET是两个完全有序集的乘积，对应于拓扑数据分析中的2参数持久性。我们感兴趣的不可分解成员属于所谓的间隔模块，根据定义，该模块是poset中间隔的指示表示。虽然整个类别的间隔模块不承认这样的局部特征，但我们表明，矩形模块的子类确实承认了一个，并且从某种意义上说，这是这样做的最大的子类。
We investigate the existence of sufficient local conditions under which poset representations decompose as direct sums of indecomposables from a given class. In our work, the indexing poset is the product of two totally ordered sets, corresponding to the setting of 2-parameter persistence in topological data analysis. Our indecomposables of interest belong to the so-called interval modules, which by definition are indicator representations of intervals in the poset. While the whole class of interval modules does not admit such a local characterization, we show that the subclass of rectangle modules does admit one and that it is, in some precise sense, the largest subclass to do so.
