  Cosmic filaments are the channel through which galaxy groups assemble their
mass. Cosmic connectivity, namely the number of filaments connected to a given
group, is therefore expected to be an important ingredient in shaping group
properties.
  The local connectivity is measured in COSMOS around X-Ray detected groups
between redshift 0.5 and 1.2. To this end, large-scale filaments are extracted
using the accurate photometric redshifts of the COSMOS2015 catalogue in
two-dimensional slices of thickness 120 comoving Mpc centred on the group's
redshift. The link between connectivity, group mass and the properties of the
brightest group galaxy (BGG) is investigated. The same measurement is carried
out on mocks extracted from the lightcone of the hydrodynamical simulation
Horizon-AGN in order to control systematics.
  More massive groups are on average more connected. At fixed group mass in
low-mass groups, BGG mass is slightly enhanced at high connectivity, while in
high mass groups BGG mass is lower at higher connectivity. Groups with a
star-forming BGG have on average a lower connectivity at given mass. From the
analysis of the Horizon-AGN simulation, we postulate that different
connectivities trace different paths of group mass assembly: at high group
mass, groups with higher connectivity are more likely to have grown through a
recent major merger, which might be in turn the reason for the quenching of the
BGG. Future large-field photometric surveys, such as Euclid and LSST, will be
able to confirm and extend these results by probing a wider mass range and a
larger variety of environment.
