On the detectability of threefold degeneracies of real Hamiltonians

We investigate real quantum states which are parallel-transported around a triple degeneracy. Applying a recently proposed test [Phys. Rev. Lett. 92 (2004) 060406], it is shown that when none of the states change sign upon completing the circle, the degeneracy is detectable by topological means. Examples from deformed microwave resonators are presented to illustrate the results.