Double, über and poset homology

2025/10/12 by Ruiz, Carlos Gabriel Valenzuela
#55N35 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.10424

Abstract

We present a comparison map between the uberhomology of a simplicial complex K and the double homology of its associated moment-angle complex Z_K. We show these two homology theories differ at three bidegrees, which depend on whether the complex K is neighbourly or not.

Citations

• Sphere Triangulations and their Double Homology
• A stability theorem for bigraded persistence barcodes
• Categorifying connected domination via graph überhomology
• Filtered simplicial homology, graph dissimilarity and überhomology
• Thin Posets, CW Posets, and Categorification

Related

• Bridging between überhomology and double homology
• Double homology and wedge-decomposable simplicial complexes
• Filtered simplicial homology, graph dissimilarity and überhomology
• The homology of simplicial complement and the cohomology of the moment-angle complexes
• The Geometric Realization of a Semi-Simplicial Complex