  We study the role of cold gas in quenching star formation in the green valley
by analysing ALMA $^{12}$CO (1-0) observations of three galaxies with resolved
optical spectroscopy from the MaNGA survey. We present resolution-matched maps
of the star formation rate and molecular gas mass. These data are used to
calculate the star formation efficiency (SFE) and gas fraction ($f_{\rm~gas}$)
for these galaxies separately in the central `bulge' regions and outer disks.
We find that, for the two galaxies whose global specific star formation rate
(sSFR) deviates most from the star formation main sequence, the gas fraction in
the bulges is significantly lower than that in their disks, supporting an
`inside-out' model of galaxy quenching. For the two galaxies where SFE can be
reliably determined in the central regions, the bulges and disks share similar
SFEs. This suggests that a decline in $f_{\rm~gas}$ is the main driver of
lowered sSFR in bulges compared to disks in green valley galaxies. Within the
disks, there exist common correlations between the sSFR and SFE and between
sSFR and $f_{\rm~gas}$ on kpc scales -- the local SFE or $f_{\rm~gas}$ in the
disks declines with local sSFR. Our results support a picture in which the sSFR
in bulges is primarily controlled by $f_{\rm~gas}$, whereas both SFE and
$f_{\rm~gas}$ play a role in lowering the sSFR in disks. A larger sample is
required to confirm if the trend established in this work is representative of
green valley as a whole.
