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R\'enyi and entanglement entropies are constructed for 2d q-deformedtopological Yang-Mills theories with gauge group $U(N)$, as well as the dual 3dChern-Simons (CS) theory on Seifert manifolds. When $q=\exp[2\pi i/(N+K)]$, and$K$ is odd, the topological R\'enyi entropy and Wilson line observables of theCS theory can be expressed in terms of the modular transformation matrices ofthe WZW theory, $\rm{\hat{U}(N)}_{K,N(K+N)}$. If both $K$ and $N$ are odd,there is a level-rank duality of the 2d qYM theory and of the associated CStheory, as well as that of the R\'enyi and entanglement entropies, and Wilsonline observables.

Topological R\'enyi and Entanglement Entropy for a 2d q-deformed $U(N)$ Yang-Mills theory and its Chern-Simons dual