2022/09/02 by İsmail Güzel, Güzel, İsmail, Atabey Kaygun +1
Computer Science · Mathematics · #05B35 #55N31 #57R90 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2209.01099
openalex publication_date 2022/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.