  We study three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories on
$\mathcal{M}_{g,p}$, an oriented circle bundle of degree $p$ over a closed
Riemann surface, $\Sigma_g$. We compute the $\mathcal{M}_{g,p}$ supersymmetric
partition function and correlation functions of supersymmetric loop operators.
This uncovers interesting relations between observables on manifolds of
different topologies. In particular, the familiar supersymmetric partition
function on the round $S^3$ can be understood as the expectation value of a
so-called "fibering operator" on $S^2 \times S^1$ with a topological twist.
More generally, we show that the 3d $\mathcal{N}=2$ supersymmetric partition
functions (and supersymmetric Wilson loop correlation functions) on
$\mathcal{M}_{g,p}$ are fully determined by the two-dimensional A-twisted
topological field theory obtained by compactifying the 3d theory on a circle.
We give two complementary derivations of the result. We also discuss
applications to F-maximization and to three-dimensional supersymmetric
dualities.
