Séminaire Gaston Darboux :

Le 20 mai 2022 à 9:45 - salle 109

Présentée par Hiang Jingyin - Ohio State University

Morse quasiflats

In the 1980s, Gromov introduced the notion of hyperbolic metric spaces and groups by axiomatizing fundamental geometric properties of the negatively curved spaces. However, one repeatedly see traces of Gromov hyperbolicity in many examples of groups and spaces which are far from being negatively curved. This leads to several different attempts of developing ``generalized hyperbolicity''. Motivated by questions on the geometry and rigidity of non-positively curved spaces and groups, we introduced the notion of Morse quasiflats, which is a higher dimensional versions of Gromov hyperbolicity. The goal of this talk is to explain this notion, its motivations and examples. We also show that as a key property, these quasiflats are asymptotically conical, and hints potential applications to group theory. Based on joint work with B. Kleiner and S. Stadler.