  Symplectic Khovanov homology is an invariant of oriented links defined by
Seidel and Smith and conjectured to be isomorphic to Khovanov homology. I
define morphisms (up to a global sign ambiguity) between symplectic Khovanov
homology groups, corresponding to isotopy classes of smooth link cobordisms in
4D between a fixed pair of links. These morphisms define a functor from the
category of links and such cobordisms to the category of abelian groups and
group homomorphisms up to a sign ambiguity. This provides an extra structure
for symplectic Khovanov homology and more generally an isotopy invariant of
smooth surfaces in 4D; a first step in proving the conjectured isomorphism of
symplectic Khovanov homology and Khovanov homology. The maps themselves are
defined using a generalisation of Seidel's relative invariant of exact
Lefschetz fibrations to exact Morse-Bott-Lefschetz fibrations with non-compact
singular loci.
