  The purpose of this paper is to interpret polynomial invariants of strongly
invertible links in terms of Khovanov homology theory. To a divide, that is a
proper generic immersion of a finite number of copies of the unit interval and
circles in a 2-disc, one can associate a strongly invertible link in the
3-sphere. This can be generalized to signed divides : divides with + or - sign
assignment to each crossing point. Conversely, to any link $L$ that is strongly
invertible for an involution $j$, one can associate a signed divide. Two
strongly invertible links that are isotopic through an isotopy respecting the
involution are called strongly equivalent. Such isotopies give rise to moves on
divides. In a previous paper of the author, one can find an exhaustive list of
moves that preserves strong equivalence, together with a polynomial invariant
for these moves, giving therefore an invariant for strong equivalence of the
associated strongly invertible links. We prove in this paper that this
polynomial can be seen as the graded Euler characteristic of a graded complex
of vector spaces. Homology of such complexes is invariant for the moves on
divides and so is invariant through strong equivalence of strongly invertible
links.
