A fibered Tukia theorem for nilpotent Lie groups

Tullia Dymarz, David Fisher, Xiangdong Xie

Published 2023-04-25Version 1

We establish a Tukia-type theorem for uniform quasiconformal groups of a Carnot group. More generally we establish a fiber bundle version (or foliated version) of Tukia theorem for uniform quasiconformal groups of a nilpotent Lie group whose Lie algebra admits a diagonalizable derivation with positive eigenvalues. These results have applications to quasi-isometric rigidity of solvable groups [DFX].