Plane curves and bialgebra of Lagrangian subspaces

25 pages, 15 figuresInternational audienceWe study multicomponent plane curves with possible singularities of selftangency type. To each such curve 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 for the framed chord diagram of a one-component plane curve. Moreover, the actions of Morse perestroikas and Vassiliev moves 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