We define a persistent cohomology invariant called persistent cup-length which is able to extract non trivial information about the evolution of the cohomology ring structure across a filtration. We also devise algorithms for the computation of this invariant and we furthermore show that the persistent cup-length is 2-Lipschitz continuous with respect to the homotopy interleaving and Gromov-Hausdorff distances.

中文翻译：

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持久杯长不变量

我们定义了一个持久的上同调不变量，称为持久杯长度，它能够提取有关跨过滤的上同调环结构演变的重要信息。我们还设计了用于计算此不变量的算法，并且我们进一步表明，关于同伦交织和 Gromov-Hausdorff 距离，持久杯长度是 2-Lipschitz 连续的。