  A geometric theory of brane-worlds with large or non-compact extra dimensions
is presented. It is shown that coordinate gauge independent perturbations of
the brane-world correspond to the Einstein-Hilbert dynamics derived from the
embeddings of the brane-world. The quantum states of a perturbation are
described by Schr\"odinger's equation with respect to the extra dimensions and
the deformation Hamiltonian. A gauge potential with confined components is
derived from the differentiable structure of the brane-world
