  We use images of high spatial, spectral and temporal resolution, obtained
using both ground- and space-based instrumentation, to investigate the coupling
between wave phenomena observed at numerous heights in the solar atmosphere.
Intensity oscillations of 3 minutes are observed to encompass photospheric
umbral dot structures, with power at least three orders-of-magnitude higher
than the surrounding umbra. Simultaneous chromospheric velocity and intensity
time series reveal an 87 \pm 8 degree out-of-phase behavior, implying the
presence of standing modes created as a result of partial wave reflection at
the transition region boundary. An average blue-shifted Doppler velocity of
~1.5 km/s, in addition to a time lag between photospheric and chromospheric
oscillatory phenomena, confirms the presence of upwardly-propagating slow-mode
waves in the lower solar atmosphere. Propagating oscillations in EUV intensity
are detected in simultaneous coronal fan structures, with a periodicity of 172
\pm 17 s and a propagation velocity of 45 \pm 7 km/s. Numerical simulations
reveal that the damping of the magneto-acoustic wave trains is dominated by
thermal conduction. The coronal fans are seen to anchor into the photosphere in
locations where large-amplitude umbral dot oscillations manifest. Derived
kinetic temperature and emission measure time-series display prominent
out-of-phase characteristics, and when combined with the previously established
sub-sonic wave speeds, we conclude that the observed EUV waves are the coronal
counterparts of the upwardly-propagating magneto-acoustic slow-modes detected
in the lower solar atmosphere. Thus, for the first time, we reveal how the
propagation of 3 minute magneto-acoustic waves in solar coronal structures is a
direct result of amplitude enhancements occurring in photospheric umbral dots.
