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During the EoR, the first stars and galaxies appear while creating ionizedbubbles that will eventually percolate near z=6. These ionized bubbles andpercolation process are nowadays under a lot of scrutiny since observations ofthe HI gas will be carried on in the next decade with e.g. the SKAradiotelescope. Studies of the EoR are performed on semi-analytical and fullynumerical cosmological simulations to investigate e.g. the topology of theprocess. We analyse the topology of EoR models through regions that are underthe radiative influence of ionization sources. They are associated with peakpatches of reionization redshift (zreion) field, for which we measure theirgeneral properties (e.g. number, size, shape, orientation). We aim at gaininginsights on the geometry of the reionization process and how it relates to thematter distribution for example. We also assess how such measurements can beused to quantify the influence of physical parameters on the reionizationmodels or the differences between fully numerical simulations andsemi-analytical models. We use the DisPerSE framework (which applies the Morsetheory and the persistent homology) on different EoR scenarios through gasdensity and zreion maps. We find that we can distinguish between EoR modelswith different sources using simple analyses on the number, shape and sizedistributions of the peak patches. For every model, we statistically show thatthey are rather prolate and aligned with the gas filaments. We brieflyhighlight that the percolation process can be followed studying zreion fieldswith different persistence thresholds. We show that fully numerical EMMAsimulations can be made consistent with 21cmFAST models in this topologicalframework as long as the source distribution is diffuse enough.

A first look at the topology of reionization redshifts in models of the Epoch of the Reionization