What triggers galaxy transformations? The environments of post-starburst galaxies

(abridged) There are good observational reasons to believe that the progenitors of red galaxies have undergone starbursts, followed by a post-starburst phase. We investigate the environments of post-starburst galaxies by measuring \textsl{(1)} number densities in $8 h^{-1} \mathrm{Mpc}$ radius comoving spheres, \textsl{(2)} transverse distances to nearest Virgo-like galaxy clusters, and \textsl{(3)} transverse distances to nearest luminous-galaxy neighbors. We compare the post-starburst galaxies to currently star-forming galaxies identified solely by A-star excess or $\Halpha$ emission. We find that post-starburst galaxies are in the same kinds of environments as star-forming galaxies; this is our ``null hypothesis''. More importantly, we find that at each value of the A-star excess, the star-forming and post-starburst galaxies lie in very similar distributions of environment. The only deviations from our null hypothesis are barely significant: a slight deficit of post-starburst galaxies (relative to the star-forming population) in very low-density regions, a small excess inside the virial radii of clusters, and a slight excess with nearby neighbors. None of these effects is strong enough to make the post-starburst galaxies a high-density phenomenon, or to argue that the starburst events are primarily triggered by external tidal impulses (e.g., from close passages of massive galaxies). The small excess inside cluster virial radii suggests that some post-starbursts are triggered by interactions with the intracluster medium, but this represents a very small fraction of all post-starburst galaxies.