Galaxy And Mass Assembly (GAMA): The galaxy luminosity function within
  the cosmic web
  We investigate the dependence of the galaxy luminosity function on geometric
environment within the Galaxy And Mass Assembly (GAMA) survey. The tidal tensor
prescription, based on the Hessian of the pseudo-gravitational potential, is
used to classify the cosmic web and define the geometric environments: for a
given smoothing scale, we classify every position of the surveyed region,
$0.04<{z}<0.26$, as either a void, a sheet, a filament or a knot. We consider
how to choose appropriate thresholds in the eigenvalues of the Hessian in order
to partition the galaxies approximately evenly between environments. We find a
significant variation in the luminosity function of galaxies between different
geometric environments; the normalisation, characterised by $\phi^{*}$ in a
Schechter function fit, increases by an order of magnitude from voids to knots.
The turnover magnitude, characterised by $M^*$, brightens by approximately
$0.5$ mag from voids to knots. However, we show that the observed modulation
can be entirely attributed to the indirect local-density dependence. We
therefore find no evidence of a direct influence of the cosmic web on the
galaxy luminosity function.
