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Some time-reversal symmetric topological orders are anomalous in that theycannot be realized in strictly two-dimensions without breaking time reversalsymmetry; instead, they can only be realized on the surface of certainthree-dimensional systems. We propose two quantities, which we call {\itanomaly indicators}, that can detect if a time-reversal symmetric topologicalorder is anomalous in this sense. Both anomaly indicators are expressed interms of the quantum dimensions, topological spins, and time-reversalproperties of the anyons in the given topological order. The first indicator,$\eta_2$, applies to bosonic systems while the second indicator, $\eta_f$,applies to fermionic systems in the DIII class. We conjecture that $\eta_2$,together with a previously known indicator $\eta_1$, can detect the two known$\mathbb Z_2$ anomalies in the bosonic case, while $\eta_f$ can detect the$\mathbb Z_{16}$ anomaly in the fermionic case.

Anomaly indicators for time-reversal symmetric topological orders