论文标题
持续的同源性，矩形和辅助主义
Persistent Homology, Matroids and Cobordisms
论文作者
论文摘要
关于阳性实数的poset上过滤的简单复合物的同源信息通常由描述相关betti数字的演变的条形码提供。但是，与过滤的复合物的同源类别相关联，有一个非常复杂的组合物，并且不仅可以在索引poset上计数它们。在这里，我们表明，这种组合信息可以由滤过的森林编码，甚至更好。我们还表明，这些根生的森林可以被视为恢复主义。
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.
