  We show that a Fermi surface reconstruction due to spiral antiferromagnetic
order may explain the rapid change in the Hall number as recently observed near
optimal doping in cuprate superconductors [Badoux~\textit{et. al.}, Nature
\textbf{531}, 210 (2016)]. The single-particle spectral function in the spiral
state exhibits hole pockets which look like Fermi arcs due to a strong momentum
dependence of the spectral weight. Adding charge-density wave order further
reduces the Fermi surface to a single electron pocket. We propose quantum
oscillation measurements to distinguish between commensurate and spiral
antiferromagnetic order. Similar results apply to certain metals in which
topological order replaces antiferromagnetic order.
