Measuring the topology of reionization with Betti numbers

Understand

The distribution of ionised hydrogen during the epoch of reionization (EoR) has a complex morphology.

• We propose to measure the three-dimensional topology of ionised regions using the Betti numbers.
• These quantify the topology using the number of components, tunnels and cavities in any given field.
• Based on the results for a set of reionization simulations we find that the Betti numbers of the ionisation field show a characteristic evolution during reionization, with peaks in the different Betti numbers characterising different stages of the process.