  Post-starbursts are galaxies in transition from the blue cloud to the red
sequence. Although they are rare today, integrated over time they may be an
important pathway to the red sequence. This work uses SDSS, GALEX, and WISE
observations to identify the evolutionary sequence from starbursts to fully
quenched post-starbursts in the narrow mass range $\log M(M_\odot) =
10.3-10.7$, and identifies "transiting" post-starbursts which are intermediate
between these two populations. In this mass range, $\sim 0.3\%$ of galaxies are
starbursts, $\sim 0.1\%$ are quenched post-starbursts, and $\sim 0.5\%$ are the
transiting types in between. The transiting post-starbursts have stellar
properties that are predicted for fast-quenching starbursts and morphological
characteristics that are already typical of early-type galaxies. The AGN
fraction, as estimated from optical line ratios, of these post-starbursts is
about 3 times higher ($\gtrsim 36 \pm 8 \%$) than that of normal star-forming
galaxies of the same mass, but there is a significant delay between the
starburst phase and the peak of nuclear optical AGN activity (median age
difference of $\gtrsim 200 \pm 100$ Myr), in agreement with previous studies.
The time delay is inferred by comparing the broad-band near NUV-to-optical
photometry with stellar population synthesis models. We also find that
starbursts and post-starbursts are significantly more dust-obscured than normal
star-forming galaxies in the same mass range. About $20\%$ of the starbursts
and $15\%$ of the transiting post-starbursts can be classified as the
"Dust-Obscured Galaxies" (DOGs), while only $0.8\%$ of normal galaxies are
DOGs.The time delay between the starburst phase and AGN activity suggests that
AGN do not play a primary role in the original quenching of starbursts but may
be responsible for quenching later low-level star formation during the
post-starburst phase.
