  In [Duke Math. J. 101 (1999) 359-426], Mikhail Khovanov constructed a
homology theory for oriented links, whose graded Euler characteristic is the
Jones polynomial. He also explained how every link cobordism between two links
induces a homomorphism between their homology groups, and he conjectured the
invariance (up to sign) of this homomorphism under ambient isotopy of the link
cobordism. In this paper we prove this conjecture, after having made a
necessary improvement on its statement. We also introduce polynomial Lefschetz
numbers of cobordisms from a link to itself such that the Lefschetz polynomial
of the trivial cobordism is the Jones polynomial. These polynomials can be
computed on the chain level.
