Morse theory is a powerful tool to study the topology of real manifolds. After recalling its basic features, we will discuss the existence, on complex manifolds, of holomorphic functions giving similar information on the topology. More specifically, we will review the notions of pseudoconvexity and of Stein manifold so as to gradually explain the significance of a recent result, jointly obtained with John Pardon, which shows that any Stein domain can be presented as a Lefschetz fibration over the disk. The talk will be aimed at a general mathematical audience.
Groupe d’études et de recherche en analyse des décisions