  We construct open symplectic manifolds which are convex at infinity
("Liouville manifolds") and which are diffeomorphic, but not symplectically
isomorphic, to cotangent bundles T^*S^{n+1}, for any n+1 \geq 3.
  These manifolds are constructed as total spaces of Lefschetz fibrations,
where the fibre and all but one of the vanishing cycles are fixed. We show that
almost any choice of the last vanishing cycle leads to a nonstandard symplectic
structure (those choices which yield standard T^*S^{n+1} can be exactly
determined).
  The Corrigendum changes the statement and proof of Lemma 1.1 in the original
paper, which corrects our original description of the diffeomorphism type of
the manifolds. We also fill a gap in the original proof of Lemma 1.2.
