Characteristic Topological Invariants

2023/02/06 by Oliver Knill, Knill, Oliver · 2 citations
Computer Science · Mathematics · #55U10 #57M15 #68R10 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2302.02510

openalex publication_date 2023/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The higher characteristics w_m(G) for a finite abstract simplicial complex G are topological invariants that satisfy k-point Green function identities and can be computed in terms of Euler characteristic in the case of closed manifolds, where we give a new proof of w_m(G)=w₁(G). Also the sphere formula generalizes: for any simplicial complex, the total higher characteristics of unit spheres at even dimensional simplices is equal to the total higher characteristic of unit spheres at odd dimensional simplices.

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Related

• The Sphere Formula
• Unusual formulae for the Euler characteristic
• Sphere geometry and invariants
• Higher Euler characteristics
• The Cohomology for Wu Characteristics