  The abelian Chern-Simons theory is considered on a cylindrical spacetime
$\mathbb{R} \times D$, in a not necessarily flat Lorentzian background. As in
the flat bulk case with planar boundary, we find that also on the radial
boundary of a curved background a Ka\c{c}-Moody algebra exists, with the same
central charge as in the flat case, which henceforth depends neither on the
bulk metric nor on the geometry of the boundary. The holographically induced
theory on the 2D boundary is topologically protected, in the sense that it
describes a Luttinger liquid, no matter which the bulk metric is. The main
result of this paper is that a remnant of the 3D bulk theory resides in the
chiral velocity of the edge modes, which is not a constant like in the flat
bulk case, but it is local, depending on the determinant of the induced metric
on the boundary. This result may provide a theoretical framework for the
recently observed accelerated chiral bosons on the edge of some Hall systems.
