Matrix Invariants as Homotopy Invariants in Finite T₀-spaces

2025/06/20 by Chocano, Pedro J. · 2 citations
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2506.16861

openalex publication_date 2025/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a bijection between the set of finite topological T₀-spaces (or partially ordered sets) and equivalence classes of square matrices. The absolute value of the determinant or the rank of these matrices serve as simple homotopy invariants for the corresponding topological spaces, and consequently, for finite simplicial complexes. To conclude, we explore further relationships and problems concerning finite posets within the context of these matrices.

Citations

• A formula for the Euler characteristic of a poset through the determinant of the order-complement matrix
• Simple Homotopy Types and Finite Spaces

Cited by

• A formula for the Euler characteristic of a poset through the determinant of the order-complement matrix
• Riordan pattern's quest within simplicial complexes

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