  In dimensions congruent to 1 modulo 4, we prove that the cotangent bundle of
an exotic sphere which does not bound a parallelisable manifold is not
symplectomorphic to the cotangent bundle of the standard sphere. More
precisely, we prove that such an exotic sphere cannot embed as a Lagrangian in
the cotangent bundle of the standard sphere. The main ingredients of the
construction are (1) the fact that the graph of the Hopf fibration embeds the
standard sphere, and hence any Lagrangian which embeds in its cotangent bundle,
as a displaceable Lagrangian in the product a symplectic vector space of the
appropriate dimension with its complex projective space, and (2) a moduli space
of solutions to a perturbed Cauchy-Riemann equation introduced by Gromov.
