  I examine the relationship between $(d+1)$-dimensional Poincar\'e metrics and
$d$-dimensional conformal manifolds, from both mathematical and physical
perspectives. The results have a bearing on several conceptual issues relating
to asymptotic symmetries, in general relativity and in gauge-gravity duality,
as follows:
  (1: Ambient Construction) I draw from the remarkable work by Fefferman and
Graham (1985, 2012) on conformal geometry, in order to prove two propositions
and a theorem that characterise the classes of diffeomorphisms that qualify as
gravity-invisible. I define natural notions of gravity-invisibility (strong,
weak, and simpliciter) which apply to the diffeomorphisms of Poincar\'e metrics
in any dimension.
  (2: Dualities) I apply the notions of invisibility to gauge-gravity
dualities: which, roughly, relate Poincar\'e metrics in $d+1$ dimensions to
QFTs in $d$ dimensions. I contrast QFT-visible vs. QFT-invisible
diffeomorphisms: those gravity diffeomorphisms that can, respectively cannot,
be seen from the QFT.
  The QFT-invisible diffeomorphisms are the ones which are relevant to the hole
argument in Einstein spaces. The results on dualities are surprising, because
the class of QFT-visible diffeomorphisms is larger than expected, and the class
of QFT-invisible ones is smaller than expected, or usually believed, i.e.
larger than the PBH diffeomorphisms in Imbimbo et al. (2000). I also give a
general derivation of the asymptotic conformal Killing equation, which has not
appeared in the literature before.
