Denis Auroux, Ecole Polytechnique
Branched coverings, Luttinger surgery and non-isotopy

In contrast with the spectacular progress made on the symplectic isotopy problem for smooth curves in the complex projective plane, various instances of non-isotopy phenomena for symplectic curves in complex surfaces have been discovered over the recent years. Using branched coverings as our main tool, we show that these examples can be reinterpreted in terms of surgery operations along Lagrangian tori in symplectic 4-manifolds. Various examples will be discussed, relating the study of symplectic curves in complex surfaces to that of symplectic 4-manifolds and their topological invariants.