2024/11/13 by Ryoya Kai, Kai, Ryoya, Hiroshi Tamaru +1 · 1 citation
Mathematics · #Advanced Mathematical Identities #Advanced Topology and Set Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2411.08319
openalex publication_date 2024/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A quandle is an algebraic system whose axioms generalize the algebraic structure of the point symmetries of symmetric spaces. In this paper, we give a definition of Euler characteristics for quandles. In particular, the quandle Euler characteristic of a compact connected Riemannian symmetric space coincides with the topological Euler characteristic. Additionally, we calculate the Euler characteristics of some finite quandles, including generalized Alexander quandles, core quandles, discrete spheres, and discrete tori. Furthermore, we prove several properties of quandle Euler characteristics, which suggest that they share similar properties with topological Euler characteristics.