Data

"Two-numbers and Euler characteristics for quandles", 8th Tunisian-Japanese Conference: Geometric and Harmonic Analysis on Homogeneous Spaces and Applications in Honor of Professor Dominique Manchon (Tui Blue Manar, Hammamet), 2025/10/27

Abstract

In this talk, we will define the Euler characteristic for quandles, and introduce some of its properties and computational results. In particular, when we consider compact symmetric spaces as quandles, the Euler characteristic we have defined coincides with the usual topological Euler characteristic. Thanks to the pioneering work of Chen and Nagano, the Euler characteristics of compact symmetric spaces have been shown to relate to the notions of antipodal sets and two-numbers. Our research aims to extend this framework to quandles. The main part of this talk is based on a joint work with Ryoya Kai.

Slide

Hiroshi Tamaru; Two-numbers and Euler characteristics for quandles, 2025/10