Finite subquandles realizing symmetric-space invariants

Determine whether every compact connected Riemannian symmetric space admits a finite subquandle with the same two-number and Euler characteristic, and characterize the properties of any such finite quandle.

Background

The paper develops quandle analogues of the two-number and Euler characteristic, and constructs finite quandles that exhibit behavior both analogous and contrary to the Chen–Nagano theory.

The first explicitly posed problem asks whether every compact connected Riemannian symmetric space contains a finite subquandle simultaneously matching both numerical invariants, and, if so, what structural properties such finite quandles possess.

References

For each compact connected Riemannian symmetric space $M$, does there exists a finite subquandle $X$ of $M$ with the two-number and the same Euler characteristic? If exists, what properties such finite quandle satisfy?

— Two-numbers and Euler characteristics for quandles  (2609.05187 - Kai et al., 4 Sep 2026) in Problem 1, final Problem environment