Geodesic
A fibered Tukia theorem for nilpotent Lie groups
Tullia Dymarz1 ; David Fisher2 ; Xiangdong Xie3
1 University of Wisconsin-Madison, Department of Mathematics
2 Rice University, Department of Mathematics
3 Bowling Green State University, Department of Mathematics and Statistics
Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 653-680.

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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].  
DOI : 10.54330/afm.137788
Keywords: Uniform quasiconformal groups, uniform quasisimilarity groups, nilpotent Lie groups

Tullia Dymarz 1 ; David Fisher 2 ; Xiangdong Xie 3

1 University of Wisconsin-Madison, Department of Mathematics
2 Rice University, Department of Mathematics
3 Bowling Green State University, Department of Mathematics and Statistics 
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Tullia Dymarz; David Fisher; Xiangdong Xie. A fibered Tukia theorem for nilpotent Lie groups. Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 653-680. doi : 10.54330/afm.137788. http://geodesic.mathdoc.fr/articles/10.54330/afm.137788/

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