  We use large N-body simulations of dissipationless gravitational clustering
in cold dark matter (CDM) cosmologies to study whether the properties of dark
matter halos are affected by their environment. We look for correlations
between the masses, formation redshifts, concentrations, shapes and spins of
halos and the overdensity of their local environment. We also look for
correlations of these quantities with the local tidal field. Our conclusion is
extremely simple. Only the mass distribution varies as a function of
environment. This variation is well described by a simple analytic formula
based on the conditional Press-Schechter theory. We find no significant
dependence of any other halo property on environment. Our results do not depend
on our choice of cosmology. According to current hierarchical models, the
structure and evolutionary history of a galaxy is fully determined by the
structure and evolutionary history of the dark halo in which it is embedded. If
these models are correct, clustering variations between galaxies of differing
morphological types, luminosities, colours and surface brightnesses, must all
arise because the halo mass function is skewed towards high mass objects in
overdense regions of the Universe and towards low mass objects in underdense
regions.
