持久同调、拟阵与余序
Persistent Homology, Matroids and Cobordisms
摘要：
关于正实数偏序集上的过滤单纯复形的同调信息通常由描述相关贝蒂数演化的条形码表示。然而，有一个非常复杂的组合学与过滤复形的同调类相关，人们可以做的不仅仅是在索引偏序集上计数它们。在这里，我们表明，这种组合信息可以编码的过滤拟阵，甚至更好的是，有根森林。我们还表明，这些有根森林可以实现cobordisms。
英文摘要：
The homological information about a filtered simplicial complex over the poset of positive real numbers is often presented by a barcode which depicts the evolution of the associated Betti numbers. However, there is a wonderfully complex combinatorics associated with the homology classes of a filtered complex, and one can do more than just counting them over the index poset. Here, we show that this combinatorial information can be encoded by filtered matroids, or even better, by rooted forests. We also show that these rooted forests can be realized as cobordisms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
