  There are some similarities between cohomology of SU(2)-representation
varieties of the fundamental group of some link complements and the Khovanov
homology of the links. We start here a program to explain a possible source of
these similarities. We introduce a symplectic manifold ${\mathscr M}$ with an
action of the braid group $B_{2n}$ preserving the symplectic structure. The
action allows to associate a Lagrangian submanifold of ${\mathscr M}$ to every
braid. The representation variety of a link can then be described as the
intersection of such Lagrangian submanifolds, given a braid presentation of the
link. We expect this to go some way in explaining the similarities mentioned
above.
