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Invariants for tame parametrised chain complexes
Homology, Homotopy and Applications ( IF 0.5 ) Pub Date : 2021-06-09 , DOI: 10.4310/hha.2021.v23.n2.a11 Wojciech Chachólski 1 , Barbara Giunti 2 , Claudia Landi 2
Homology, Homotopy and Applications ( IF 0.5 ) Pub Date : 2021-06-09 , DOI: 10.4310/hha.2021.v23.n2.a11 Wojciech Chachólski 1 , Barbara Giunti 2 , Claudia Landi 2
Affiliation
We set the foundations for a new approach to Topological Data Analysis (TDA) based on homotopical methods at the chain complex 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.
中文翻译:
驯服参数化链复合体的不变量
我们为基于链复杂级别的同伦方法的拓扑数据分析 (TDA) 新方法奠定了基础。我们将驯服参数化链复合体的类别呈现为一个综合环境,其中包括通常 TDA 单独处理的几种情况,例如持久性模块、锯齿形模块和交换阶梯。我们使用模型结构和各种最小共纤剂近似值提取此类别中的新不变量。这种近似及其不变量保留了它们近似的对象的一些拓扑方面,而不仅仅是同源方面。
更新日期:2021-06-10
中文翻译:
驯服参数化链复合体的不变量
我们为基于链复杂级别的同伦方法的拓扑数据分析 (TDA) 新方法奠定了基础。我们将驯服参数化链复合体的类别呈现为一个综合环境,其中包括通常 TDA 单独处理的几种情况,例如持久性模块、锯齿形模块和交换阶梯。我们使用模型结构和各种最小共纤剂近似值提取此类别中的新不变量。这种近似及其不变量保留了它们近似的对象的一些拓扑方面,而不仅仅是同源方面。