  Recently, a new procedure to quantize the $SU(N)$ Yang-Mills theory in the
nonperturbative regime was proposed. The idea is to divide the configuration
space $\{A_\mu\}$ into sectors labeled by different topological degrees of
freedom and fix the gauge separately on each one of them. As Singer's theorem
on gauge copies only refers to gauge fixing conditions that are global in
$\{A_\mu\}$, this construction might avoid the Gribov problem. In this work, we
present a proof of the renormalizability in the center-vortex sectors, thus
establishing the calculability of the Yang-Mills center-vortex ensemble.
