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We study the influence of the ambient large-scale cold-gas vorticity on thespecific star formation rate (sSFR) of central galaxies with stellar masses of$10.0<\log\,M_{\ast}/\mathrm{M_{\odot}}<11.5$ at $z=0$, using the TNG100simulation. The cold-gas vorticity defined and calculated for gas with $T_{\rmgas} < 2\times 10^4 \mathrm{K}$ and on scales of $\sim$ 1 Mpc can well describethe angular motion of the ambient cold gas. We find crucial evidence forconnections between the cold-gas vorticity and star-formation activeness, suchthat at any given halo mass (particularly below $10^{13}\,\mathrm{M_{\odot}}$),galaxies living in higher cold-gas vorticity environments are generally lessstar-forming, regardless of their large-scale environment types (filament orknot), or star formation states (star-forming or quenched). Specifically, at afixed halo mass scale of $10^{12}-10^{13}\,\mathrm{M_{\odot}}$, the median sSFRof galaxies living in environments with the top 30\% cold-gas vorticity is$\sim 0.5$ dex below that of galaxies living in environments with the bottom30\% cold-gas vorticity. At any fixed halo mass scale, cold-gas vorticitiesaround filament galaxies are generally higher than those around knot galaxies,consistent with that filament galaxies have lower sSFRs than knot galaxies.This large-scale cold-gas vorticity is highly connected to the orbital angularmomentum of neighboring galaxies up to a distance of $\sim$ 500 kpcs,indicating their common origin and a possible angular momentuminheritance/modulation from the latter to the former. The negative modulationby the environmental vorticity to galaxy star formation is only significantlyobserved for the cold gas, indicating the unique role of cold-gas angularmomentum.

From larger-scale cold-gas angular-momentum environment to galaxy star-formation activeness