Mathematics Colloquia and Seminars

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A real algebraic curve in a 3-dimensional real algebraic variety can be considered as a link. One can ask about topological properties of the links which appear when the complexification of the curve belongs to a certain family of curves. On the other hand, for each irreducible family of real algebraic curves in a 3-dimensional non-singular real algebraic variety, one can modify the usual notions and questions of the classical link theory by taking into account the algebraic nature of the curves. Say, abient isotopy turns into deformation in the same family of non-singular real algebraic curves. The answers to these questions (when known) involve details, which do not appear in the classical link theory. We will discuss the theories that emerge in this way.