On the Euler characteristics for quandles
Geometric Topology
2024-11-14 v1 Differential Geometry
Group Theory
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.
Cite
@article{arxiv.2411.08319,
title = {On the Euler characteristics for quandles},
author = {Ryoya Kai and Hiroshi Tamaru},
journal= {arXiv preprint arXiv:2411.08319},
year = {2024}
}