“Lefschetz pencils and the symplectic topology of complex surfaces”
Denis Auroux, Massachusetts Institute of Technology

Abstract:
In this talk, we will review symplectic Lefschetz pencils and the use of their monodromy invariants to study the topology of symplectic 4-manifolds. In particular, we will outline an approach based on Lefschetz pencils to study the symplectic topology of Horikawa surfaces: this is a pair of complex surfaces of general type which are known to be homeomorphic but not deformation equivalent, and about which it is unknown whether they are diffeomorphic or, equipped with their canonical Kahler forms, symplectomorphic. While the results so far are insufficient to conclude one way or the other, Lefschetz pencils shed new light on the question.