  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.
