CRM: Centro De Giorgi
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Sub-riemannian geometry and beyond, III

Tukia type theorems for Carnot-by-Carnot groups I (joint seminar with Tullia Dymarz)

speaker: David Fisher (Indiana University Bloomington)

abstract: Motivated by Mostow's proof of Mostow rigidity, Tukia proved landmark results about when a group of quasi-conformal mappings of $\mathbb{R}n$ is quasiconformally conjugate to a conformal action. Gromov later pointed out that Tukia's theorem had fairly immediate consequences for the quasi-isometric rigidity of fundamental groups of hyperbolic manifolds. In these talks we will discuss recent generalizations of Tukia's theorem to a broader class of spaces, namely what we call Carnot-by-Carnot groups. The motivation for studying this class of spaces (and even broader ones) also comes from the study of quasi-isometric rigidity for certain groups and spaces. This work is joint with Xie.

Wed 21 Jun, 10:30 - 11:30, Aula Dini
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