Ressource pédagogique : Robert Haslhofer - The moduli space of 2-convex embedded spheres
Présentation de: Robert Haslhofer - The moduli space of 2-convex embedded spheres
Informations pratiques sur cette ressource
Droits réservés à l'éditeur et aux auteurs. CC BY-NC-ND 4.0
Description de la ressource pédagogique
Description (résumé)
We investigate the topology of the space of smoothly embedded n-spheres in R^{n+1}, i.e. the quotient space M_n:=Emb(S^n,R^{n+1})/Diff(S^n). By Hatcher’s proof of the Smale conjecture, M_2 is contractible. This is a highly nontrivial theorem generalizing in particular the Schoenflies theorem and Cerf’s theorem. In this talk, I will explain how geometric analysis can be used to study the topology of M_n respectively some of its variants.I will start by sketching a proof of Smale’s theorem that M_1 is contractible. By a beautiful theorem of Grayson, the curve shortening flow deforms any closed embedded curve in the plane to a round circle, and thus gives a geometric analytic proof of the fact that M_1 is path-connected. By flowing, roughly speaking, all curves simultaneously, one can improve path-connectedness to contractibility.In the second half of my talk, I’ll describe recent work on space of smoothly embedded spheres in the 2-convex case, i.e. when the sum of the two smallest principal curvatures is positive. Our main theorem (joint with Buzano and Hershkovits) proves that this space is path-connected, for every n. The proof uses mean curvature flow with surgery.
"Domaine(s)" et indice(s) Dewey
- Mathématiques (510)
Thème(s)
Document(s) annexe(s) - Robert Haslhofer - The moduli space of 2-convex embedded spheres
- Cette ressource fait partie de
EN SAVOIR PLUS
-
Identifiant de la fiche
24218 -
Identifiant
oai:canal-u.fr:24218 -
Schéma de la métadonnée
- LOMv1.0
- LOMFRv1.0
- Voir la fiche XML
-
Entrepôt d'origine