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.

翻译：我们定义了一种持久性的共生学变量,叫做持久性的杯长,它能够从过滤中提取出有关共生环结构演变的非微小信息。 我们还设计了计算这种异质的算法,我们进一步表明,持久性的杯长与同质性内分解和格罗莫夫-豪斯多夫的距离是连续的2-利普施茨。