  The most prodigious starburst galaxies are absent in massive galaxy clusters
today, but their connection with large scale environments is less clear at
$z\gtrsim2$. We present a search of large scale structure around a galaxy
cluster core at $z=2.095$ using a set of spectroscopically confirmed galaxies.
We find that both color-selected star-forming galaxies (SFGs) and dusty
star-forming galaxies (DSFGs) show significant overdensities around the
$z=2.095$ cluster. A total of 8 DSFGs (including 3 X-ray luminous active
galactic nuclei, AGNs) and 34 SFGs are found within a 10 arcmin radius
(corresponds to $\sim$15 cMpc at $z\sim2.1$) from the cluster center and within
a redshift range of $\Delta z=0.02$, which leads to galaxy overdensities of
$\delta_{\rm DSFG}\sim12.3$ and $\delta_{\rm SFG}\sim2.8$. The cluster core and
the extended DSFG- and SFG-rich structure together demonstrate an active
cluster formation phase, in which the cluster is accreting a significant amount
of material from large scale structure while the more mature core may begin to
virialize. Our finding of this DSFG-rich structure, along with a number of
other protoclusters with excess DSFGs and AGNs found to date, suggest that the
overdensities of these rare sources indeed trace significant mass
overdensities. However, it remains puzzling how these intense star formers are
triggered concurrently. Although an increased probability of galaxy
interactions and/or enhanced gas supply can trigger the excess of DSFGs, our
stacking analysis based on 850 $\mu$m images and morphological analysis based
on rest-frame optical imaging do not show such enhancements of merger fraction
and gas content in this structure.
