Weighted Simplicial Complexes and Weighted Analytic Torsions

2021/03/07 by Shiquan Ren, Chengyuan Wu, Ren, Shiquan +1
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2103.04252

openalex publication_date 2021/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A weighted simplicial complex is a simplicial complex with values (called weights) on the vertices. In this paper, we consider weighted simplicial complexes with ℝ²-valued weights. We study the weighted homology and the weighted analytic torsion for such weighted simplicial complexes.

Citations

• Homologies of path complexes and digraphs
• Torsion of digraphs and path complexes
• Weighted Analytic Torsion for Weighted Digraphs

Related

• On Weighted Simplicial Homology
• A computational framework for weighted simplicial homology
• Weighted Analytic Torsion for Weighted Digraphs
• Hodge Decompositions for Weighted Hypergraphs
• On algebraic and combinatorial properties of weighted simplicial complexes