Delphine Moussard

A famous theorem of Laudenbach and Poénaru says that any diffeomorphism of the boundary of a 4-dimensional 1-handlebody extends to a  diffeomorphism of the whole handlebody. After recalling why this is essential in the theory of closed smooth 4-manifolds, I will present a new proof of  this result using Heegaard splittings. If time permits, I will also give a generalization of this theorem to compression bodies.