  We examine the HI-to-stellar mass ratio (HI fraction) for galaxies near
filament backbones within the nearby Universe ($d <$ 181 Mpc). This work uses
the 6 degree Field Galaxy Survey and the Discrete Persistent Structures
Extractor to define the filamentary structure of the local cosmic web. HI
spectral stacking of HI Parkes all sky survey observations yields the HI
fraction for filament galaxies and a field control sample. The HI fraction is
measured for different stellar masses and fifth nearest neighbour projected
densities ($\Sigma_{5}$) to disentangle what influences cold gas in galaxies.
For galaxies with stellar masses log($M_{\star}$) $<$ 11 M$_{\odot}$ in
projected densities 0 $\leq$ $\Sigma_{5}$ $<$ 3 galaxies Mpc$^{-2}$, all HI
fractions of galaxies near filaments are statistically indistinguishable from
the control sample. Galaxies with stellar masses log($M_{\star}$) $\geq$ 11
M$_{\odot}$ have a systematically higher HI fraction near filaments than the
control sample. The greatest difference is 0.75 dex, which is 5.5$\sigma$
difference at mean projected densities of 1.45 galaxies Mpc$^{-2}$. We suggest
that this is evidence for massive galaxies accreting cold gas from the
intrafilament medium that can replenish some HI gas. This supports cold mode
accretion where filament galaxies with a large gravitational potential can draw
gas from the large-scale structure.
