Th\'eorie de for\c{c}age des hom\'eomorphismes de surface [d'apr\`es Le Calvez et Tal]

Abstract

In 1912 Brouwer published his translation theorem, which implies, for example, that an orientation preserving homeomorphism of the plane having a periodic point also has a fixed point. This theorem has given rise to a number of developments, leading among other things to Le Calvez's proof of the existence of a Brouwer foliation for surface homeomorphisms homotopic to identity. Recently, Le Calvez and Tal used this foliation to construct a forcing theory intrinsically topological which, like Brouwer's theorem, allows to deduce the existence of new orbits from certain dynamic properties of homeomorphism. The expos{\'e} will describe the general principles of this theory, as well as some of its many applications.