  We demonstrate that the Discrete Persistent Source Extractor (DisPerSE) can
be used with spectroscopic redshifts to define the cosmic web and its distance
to galaxies in small area deepfields. Here we analyze the use of DisPerSE to
identify structure in observational data. We apply DisPerSE to the distribution
of galaxies in the COSMOS field and find the best parameters to identify
filaments. We compile a catalog of 11500 spectroscopic redshifts from the
Galaxy and Mass Assembly (GAMA) G10 data release. We analyze two-dimensional
slices, extract filaments and calculate the distance for each galaxy to its
nearest filament. We find that redder and more massive galaxies are closer to
filaments. To study the growth of galaxies across cosmic time, and environment,
we are carrying out an HI survey covering redshifts z = 0 - 0.45, the COSMOS HI
Large Extragalactic Survey (CHILES). In addition we present the predicted HI
mass fraction as a function of distance to filaments for the spectroscopically
known galaxies in CHILES. Lastly, we discuss the cold gas morphology of a few
individual galaxies and their positions with respect to the cosmic web. The
identification of the cosmic web, and the ability of CHILES to study the
resolved neutral hydrogen morphologies and kinematics of galaxies, will allow
future studies of the properties of neutral hydrogen in different cosmic web
environments across the redshift range z = 0.1 - 0.45.
