  Using a series of high-resolution N-body simulations of the concordance
cosmology we investigate how the formation histories, shapes and angular
momenta of dark-matter haloes depend on environment. We first present a
classification scheme that allows to distinguish between haloes in clusters,
filaments, sheets and voids in the large-scale distribution of matter. This
method is based on a local-stability criterion for the orbits of test particles
and closely relates to the Zel'dovich approximation. Applying this scheme to
our simulations we then find that: i) Mass assembly histories and formation
redshifts strongly depend on environment for haloes of mass M<M* (haloes of a
given mass tend to be older in clusters and younger in voids) and are
independent of it for larger masses; ii) Low-mass haloes in clusters are
generally less spherical and more oblate than in other regions; iii) Low-mass
haloes in clusters have a higher median spin than in filaments and present a
more prominent fraction of rapidly spinning objects; we identify recent major
mergers as a likely source of this effect. For all these relations, we provide
accurate functional fits as a function of halo mass and environment. We also
look for correlations between halo-spin directions and the large-scale
structures: the strongest effect is seen in sheets where halo spins tend to lie
within the plane of symmetry of the mass distribution. Finally, we measure the
spatial auto-correlation of spin directions and the cross-correlation between
the directions of intrinsic and orbital angular momenta of neighbouring haloes.
While the first quantity is always very small, we find that spin-orbit
correlations are rather strong especially for low-mass haloes in clusters and
high-mass haloes in filaments.
