Work

Eigenvalues and signature of quadratic forms associated with finite topological spaces

Year: 2025

Type: article

Abstract: Given any finite topological space X and a field K , we associate a quadratic space ( Q X , V X ) , consisting of a vector space V X over K and a quadratic form Q X : V X × V X → K , to X . The eigenvalues and signature of Q X are topological invariants of X . We study their relations with X . From this, we obtain restrictions to check whether a finite topological space can be embedded into another one. Additionally, we compute these invariants for minimal finite models of spheres and other families of finite spaces.

Source: Linear Algebra and its Applications

DOI: 10.1016/j.laa.2025.09.007

Author: Pedro J. Chocano

Institution: Universidad Rey Juan Carlos

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,230

Funder: Ministerio de Ciencia, Innovación y Universidades