  We study the topology of reionization using accurate three-dimensional
radiative transfer calculations post-processed on outputs from cosmological
hydrodynamic simulations. In our simulations, reionization begins in overdense
regions and then "leaks" directly into voids, with filaments reionizing last
owing to their combination of high recombination rate and low emissivity. This
result depends on the uniquely-biased emissivity field predicted by our
prescriptions for star formation and feedback, which have previously been shown
to account for a wide array of measurements of the post-reionization Universe.
It is qualitatively robust to our choice of simulation volume, ionizing escape
fraction, and spatial resolution (in fact it grows stronger at higher spatial
resolution) even though the exact overlap redshift is sensitive to each of
these. However, it weakens slightly as the escape fraction is increased owing
to the reduced density contrast at higher redshift. We also explore whether our
results are sensitive to commonly-employed approximations such as using
optically-thin Eddington tensors or substantially altering the speed of light.
Such approximations do not qualitatively change the topology of reionization.
However, they can systematically shift the overlap redshift by up to $\Delta
z\sim 0.5$, indicating that accurate radiative transfer is essential for
computing reionization. Our model cannot simultaneously reproduce the observed
optical depth to Thomson scattering and ionization rate per hydrogen atom at
$z=6$, which could owe to numerical effects and/or missing early sources of
ionization.
