  We use a cosmological simulation of the formation of the Local Group of
Galaxies to identify a mechanism that enables the removal of baryons from
low-mass halos without appealing to feedback or reionization. As the Local
Group forms, matter bound to it develops a network of filaments and pancakes.
This moving web of gas and dark matter drifts and sweeps a large volume,
overtaking many halos in the process. The dark matter content of these halos is
unaffected but their gas can be efficiently removed by ram-pressure. The loss
of gas is especially pronounced in low-mass halos due to their lower binding
energy and has a dramatic effect on the star formation history of affected
systems. This "cosmic web stripping" may help to explain the scarcity of dwarf
galaxies compared with the numerous low-mass halos expected in \Lambda CDM and
the large diversity of star formation histories and morphologies characteristic
of faint galaxies. Although our results are based on a single high-resolution
simulation, it is likely that the hydrodynamical interaction of dwarf galaxies
with the cosmic web is a crucial ingredient so far missing from galaxy
formation models.
