The space of barcode bases for persistence modules
The space of barcode bases for persistence modules
复制标题
持久性模块的条形码库空间
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
U. Tillmann
中科院分区：
文献类型：
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作者：
Emile Jacquard;Vidit Nanda;U. Tillmann
持久化模块的条形码充当其同构类的完整组合不变量。条形码通常通过在持久性模块上执行基的改变来提取，直到组成矩阵具有特殊形式。在这里，我们描述了一种用于计算条形码的新算法，该算法还跟踪并输出这种基础变化。我们的主要结果是一个明确的特征的转换组，发送一个条形码的基础上，另一个。武装的条码基地的整个空间的知识，我们能够表明，任何地图的持久性模块可以表示通过一个部分匹配的酒吧之间的源和目标都不承认嵌套的酒吧在其条码。我们还概括了上述的算法和结果的工作zizag模块。
The barcode of a persistence module serves as a complete combinatorial invariant of its isomorphism class. Barcodes are typically extracted by performing changes of basis on a persistence module until the constituent matrices have a special form. Here we describe a new algorithm for computing barcodes which also keeps track of, and outputs, such a change of basis. Our main result is an explicit characterisation of the group of transformations that sends one barcode basis to another. Armed with knowledge of the entire space of barcode bases, we are able to show that any map of persistence modules can be represented via a partial matching between bars provided that neither source nor target admits nested bars in its barcode. We also generalise the algorithm and results described above to work for zizag modules.