论文标题
超平面限制了不可兼容的$ n $维持续模块
Hyperplane Restrictions of Indecomposable $n$-Dimensional Persistence Modules
论文作者
论文摘要
了解不可兼容的$ n $维持续模块的结构是一个困难的问题，但是研究多疗法的基础。为此，Buchet和Escolar表明，任何有限的矩形$（N-1）$ - 维度持久模块具有有限的支持，都是对$ n $二维持久性模块的超平面限制。我们将此结果扩展到以下：如果$ m $是有限的$（n-1）$ - 维度持久模块，并具有有限的支持，则存在一个不可塑性的$ n $ n $ dimensional-dimensional-dimentional-dimentional-dimentional-dimentional-d $ m $ m'$，因此$ m $是$ m'$ $ m'$ to Apperplanplane。我们还表明，任何有限的曲折持久性模块都是限制一些不可兼容的$ 3 $维持续模块到路径上的限制。
Understanding the structure of indecomposable $n$-dimensional persistence modules is a difficult problem, yet is foundational for studying multipersistence. To this end, Buchet and Escolar showed that any finitely presented rectangular $(n-1)$-dimensional persistence module with finite support is a hyperplane restriction of an $n$-dimensional persistence module. We extend this result to the following: If $M$ is any finitely presented $(n-1)$-dimensional persistence module with finite support, then there exists an indecomposable $n$-dimensional persistence module $M'$ such that $M$ is the restriction of $M'$ to a hyperplane. We also show that any finite zigzag persistence module is the restriction of some indecomposable $3$-dimensional persistence module to a path.
