# The moduli space of 2-convex embedded spheres and tori

 Orateur: BUZANO Reto Localisation: Université de Londres Queen Mary, Royaume-Uni Type: Journée de géométrie Site: UPEC Salle: Salle P2 131, Université Paris-Est - Créteil Date de début: 29/05/2017 - 11:00 Date de fin: 29/05/2017 - 12:00

It is interesting to study the topology of the space of smoothly embedded n-spheres in $\mathbb R^{n+1}$. By Smale’s theorem, this space is contractible for $n=1$ and by Hatcher’s proof of the Smale conjecture, it is also contractible for $n=2$. These results are of great importance, generalising in particular the Schoenflies theorem and Cerf’s theorem. In this talk, I will explain how mean curvature flow with surgery can be used to study a higher-dimensional variant of these results, proving in particular that the space of two-convex embedded spheres is path-connected in every dimension $n$. We then also look at the space of two-convex embedded tori where the question is more intriguing and the result in particular depends on the dimension $n$. This is all joint work with Robert Haslhofer and Or Hershkovits.