Complete affine manifolds with an infinite amenable normal subgroup have amenable category at most their dimension, so all three topological volumes vanish.
Minimal Entropy of $3$-manifolds
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abstract
We compute the Minimal Entropy of every closed, orientable $3$-manifold, showing that its cube equals the sum of the cubes of the minimal entropies of each hyperbolic component arising from the $JSJ$ decomposition of each prime summand. As a consequence we show that the cube of the Minimal Entropy is additive with respect to both the prime and the $JSJ$ decomposition, thus concluding that for closed orientable $3$-manifolds the cube of the Minimal Entropy is proportional to the simplicity volume. This answers a conjecture asked by Anderson and Paternain for irreducible manifolds.
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Topological volumes of certain complete affine manifolds
Complete affine manifolds with an infinite amenable normal subgroup have amenable category at most their dimension, so all three topological volumes vanish.