Mathematics Colloquia and Seminars

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Tukia's theorem states that any uniform group of quasiconformal maps of the sphere that acts cocompactly on the space of distinct triples of points can be conjugated into the conformal group. This theorem is used as step in the proof of quasi-isometric rigidity for cocompact lattices in real hyperbolic spaces. Recently Eskin-Fisher-Whyte have described quasi-isometries of certain solvable Lie groups. Lattices in these Lie groups form classes of polycyclic groups. I will formulate and sketch the proof of a Tukia-like theorem which can be used to prove quasi-isometric rigidity for these lattices.