School of Mathematical Sciences

The moduli space of 2-convex embedded spheres menu

The moduli space of 2-convex embedded spheres

Reto Buzano (QMUL)
Tue, 04/10/2016 - 15:00
Maths 203
Seminar series: 

We investigate the topology of the space of smoothly embedded n-spheres in 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 geometric analysis can be used to study a higher-dimensional variant of these results. The main theorem (joint with Robert Haslhofer and Or Hershkovits) states that the space of 2-convex embedded spheres is path-connected in every dimension n. The proof uses mean curvature flow with surgery.