Using the largest cosmological reionization simulation to date (～ 24 billion particles), we use the genus curve to quantify the topology of the neutral hydrogen distribution on scales ≥ 1 Mpc h~(-1) as it evolves during cosmological reionization. We find that the reionization process proceeds primarily in an inside-out fashion, in which higher density regions become ionized earlier than lower density regions. There are four distinct topological phases: (1) pre-reionization at z approx＞ 15, when the genus curve is consistent with a Gaussian density distribution; (2) preoverlap at 10 approx＜ z approx＜ 15, during which the number of H II bubbles increases gradually with time, until percolation of H II bubbles starts to take effect (this phase is characterized by a very flat genus curve at high volume fractions); (3) overlap at 8 approx＜ z approx＜ 10, when large H II bubbles rapidly merge, manifested by a precipitous drop in the amplitude of the genus curve; and (4) postoverlap at 6 approx＜ z approx＜ 8, when H II bubbles have mostly overlapped, and the genus curve is consistent with a diminishing number of isolated neutral islands. After the end of reionization (z approx＜ 6), the genus of neutral hydrogen is consistent with Gaussian random phase, in agreement with observations.
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