  The gas supply from the cosmic web is the key to sustain star formation in
galaxies. It remains to be explored how the cosmic large-scale structure (LSS)
effects on galaxy evolution at given local environments. We examine galaxy
specific star formation rate as a function of local density in a LSS at
$z=0.735$ in the Extended Chandra Deep Field South. The LSS is mapped by 732
galaxies with $R<24$\,mag and redshift at $0.72\le z \le 0.75$ collected from
the literature and our spectroscopic observations with Magellan/IMACS,
consisting of five galaxy clusters/groups and surrounding filaments over an
area of $23.9 \times22.7$\,co-moving\,Mpc$^2$. The spread of spectroscopic
redshifts corresponds a velocity dispersion of 494\,km\,s$^{-1}$, indicating
the LSS likely to be a thin sheet with a galaxy density $\gtrsim 3.9$ times
that of the general field. These clusters/groups in this LSS mostly exhibit
elongated morphologies and multiple components connected with surrounding
filaments. Strikingly, we find that star-forming galaxies in the LSS keep star
formation at the same level as field, and show no dependence on local density
but stellar mass. Meanwhile, an increasing fraction of quiescent galaxies is
detected at increasing local density in both the LSS and the field, consistent
with the expectation that galaxy mass and local dense environment hold the key
to quench star formation. Combined together, we conclude that the cosmic
environment of the LSS overtakes the local environment in remaining galaxy star
formation to the level of the field.
