To each ribbon graph we assign a so-called L-space, which is a Lagrangian
subspace in an even-dimensional vector space with the standard symplectic form.
This invariant generalizes the notion of the intersection matrix of a chord
diagram. Moreover, the actions of Morse perestroikas (or taking a partial dual)
and Vassiliev moves on ribbon graphs are reinterpreted nicely in the language
of L-spaces, becoming changes of bases in this vector space. Finally, we define
a bialgebra structure on the span of L-spaces, which is analogous to the
4-bialgebra structure on chord diagrams.Comment: 21 pages, 13 figures. v2: major revision, Sec 2 and 3 completely
rewritten; v3: minor corrections. Final version, to appear in Journal of Knot
Theory and its Ramification