The geometry of the filamentary environment of galaxy clusters
  We construct a filament catalogue using an extension of the halo based
filament finder of Zhang et al.(2009), in a 250 Mpc/h side N-body simulation,
and study the properties of filaments ending upon or surrounding galaxy
clusters (within 10 Mpc/h). In this region, the majority of filamentary mass,
halo mass, and galaxy richness centered upon the cluster tends to lie in
sheets, which are not always coincident. Fixing a sheet width of 3 Mpc/h for
definiteness, we find the sheet orientations and (connected) filamentary mass,
halo mass and richness fractions relative to the surrounding sphere. Filaments
usually have one or more endpoints outside the sheet determined by filament or
halo mass or richness, with at least one having a large probability to be
aligned with the perpendicular of the plane. Scatter in mock cluster mass
measurements, for several observables, is often correlated with the
observational direction relative to these local sheets, most often for richness
and weak lensing, somewhat less for Compton decrement, and least often for
velocity dispersions. The long axis of the cluster also tends to lie in the
sheet andits orientiation relative to line of sight also correlates with mass
scatter.
