论文标题
温和参数链复合物的不变性
Invariants for tame parametrised chain complexes
论文作者
论文摘要
我们为基于链复合物级别的同位方法的方法设定了一种新的拓扑数据分析方法（TDA）的基础。我们将驯服的参数链复合物的类别作为一种综合环境，其中包括通常分别处理TDA的几种情况，例如持久模块，曲折模块和交换梯子。我们使用模型结构和各种最小的同伴近似值提取新的不变性。这种近似值及其不变性保留了它们近似物体的某些拓扑，而不仅仅是同源方面。
We set the foundations for a new approach to Topological Data Analysis (TDA) based on homotopical methods at chain complexes level. We present the category of tame parametrised chain complexes as a comprehensive environment that includes several cases that usually TDA handles separately, such as persistence modules, zigzag modules, and commutative ladders. We extract new invariants in this category using a model structure and various minimal cofibrant approximations. Such approximations and their invariants retain some of the topological, and not just homological, aspects of the objects they approximate.
