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We study the role of cold gas in quenching star formation in the green valleyby analysing ALMA $^{12}$CO (1-0) observations of three galaxies with resolvedoptical spectroscopy from the MaNGA survey. We present resolution-matched mapsof the star formation rate and molecular gas mass. These data are used tocalculate 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 inthe bulges is significantly lower than that in their disks, supporting an`inside-out' model of galaxy quenching. For the two galaxies where SFE can bereliably determined in the central regions, the bulges and disks share similarSFEs. This suggests that a decline in $f_{\rm~gas}$ is the main driver oflowered sSFR in bulges compared to disks in green valley galaxies. Within thedisks, there exist common correlations between the sSFR and SFE and betweensSFR and $f_{\rm~gas}$ on kpc scales -- the local SFE or $f_{\rm~gas}$ in thedisks declines with local sSFR. Our results support a picture in which the sSFRin 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 isrequired to confirm if the trend established in this work is representative ofgreen valley as a whole.

Resolved star formation and molecular gas properties of green valley galaxies: a first look with ALMA and MaNGA