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Article Dans Une Revue Journal of Knot Theory and Its Ramifications Année : 2016

Plane curves and bialgebra of Lagrangian subspaces

Résumé

We 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.

Dates et versions

hal-00955017 , version 1 (03-03-2014)

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Victor A. Kleptsyn, Evgeny Smirnov. Plane curves and bialgebra of Lagrangian subspaces. Journal of Knot Theory and Its Ramifications, 2016, 25 (12), 26 p. ⟨10.1142/S0218216516420062⟩. ⟨hal-00955017⟩
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