  In the next decade, radio telescopes like the Square Kilometer Array (SKA)
will explore the Universe at high redshift, and particularly during the Epoch
of Reionisation (EoR). The first structures emerged during this epoch, and
their radiations have reionised the previously cold and neutral gas of the
Universe creating ionised bubbles that percolate at the end of the EoR (at a
redshift of approximately 6). SKA will produce 2D images of the distribution of
the neutral gas at many redshifts, pushing us to develop tools and simulations
to understand its properties. This paper aims at measuring topological
statistics of the EoR in the "reionisation times" fields from both cosmological
and semi-analytical simulations. This field informs us about the time of
reionisation of the gas at each position, is used to probe the inhomogeneities
of reionisation histories and can possibly be extracted from 21 cm maps. We
also compare these measurements with analytical predictions from the gaussian
random field (GRF) theory. The GRF theory allows us to compute many statistics
of a field: PDFs of the field or its gradient, isocontour length, critical
point distributions, and skeleton length. We compare these theoretical
predictions to measurements made on reionisation time fields extracted from an
EMMA and a 21cmFAST simulations at 1 a cMpc/h resolution. We also compared our
results to GRFs generated from the fitted power spectra of the simulation maps.
Both EMMA and 21cmFAST reionisation time fields (treion(r)) are close to be
gaussian fields, in contrast with the 21 cm, density or ionisation fraction
that are all proven to be non-gaussian. Only accelerating ionisation fronts at
the end of the EoR seem to be a cause of small non-gaussianities in treion(r).
Overall our results indicate that an analytical description of the reionisation
percolation can be reasonably made within the framework of GRF theory.
