Year: 2025
Type: article
Abstract: 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.
Authors: Ryoya Kai, Hiroshi Tamaru
Institution: Osaka Metropolitan University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4410696501