  Located within the central region of the Galaxy, the Arches cluster appears
to be one of the youngest, densest and most massive stellar aggregates within
the Milky Way. As such it has the potential to be a uniquely instructive
laboratory for the study of star formation in extreme environments and the
physics of very massive stars. In order to determine the fundamental physical
properties of both cluster and constituent stars, we provide and analyse new
HST+VLT near-IR datasets. Stacking multiple epochs of spectroscopy results in
the deepest view of the cluster ever obtained, allowing us to to identify
candidate giant and main sequence stars for the first time. All cluster members
are found to be WNLh or O stars, with the smooth and continuous progression in
spectral morphologies from O super-/hypergiants through to the WNLh cohort
implying a direct evolutionary connection. Importantly no H-free Wolf-Rayets
are found, while no products of binary interaction/mass-transfer may be
unambiguously identified, despite the presence of massive binaries within the
Arches. We infer a main sequence turn-off around O4-5V, corresponding to
~30-38Msun, while the eclipsing binary F2 implies current masses of ~80Msun and
~60Msun for the WNLh and O hypergiant cohorts, respectively. A cluster age of
~2-3Myr is suggested by the location of the main-sequence turn-off. While the
absence of H-free Wolf-Rayets argues against the prior occurrence of SNe, such
an age does accommodate such events for exceptionally massive stars. Future
progress requires quantitative analysis of cluster members combined with
additional spectroscopic observations to better constrain the binary
population; nevertheless it is already abundantly clear that the Arches offers
an unprecedented insight into the formation, evolution and death of the most
massive stars Nature allows to form in the local universe (Abridged).
