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Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 
 

 

Quasisymmetric groups


Author: Vladimir Markovic
Journal: J. Amer. Math. Soc. 19 (2006), 673-715
MSC (2000): Primary 20H10, 37F30
DOI: https://doi.org/10.1090/S0894-0347-06-00518-2
Published electronically: January 25, 2006
MathSciNet review: 2220103
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Abstract: One of the first problems in the theory of quasisymmetric and convergence groups was to investigate whether every quasisymmetric group that acts on the sphere $\textbf {S}^{n}$, $n>0$, is a quasisymmetric conjugate of a Möbius group that acts on $\textbf {S}^{n}$. This was shown to be true for $n=2$ by Sullivan and Tukia, and it was shown to be wrong for $n>2$ by Tukia. It also follows from the work of Martin and of Freedman and Skora. In this paper we settle the case of $n=1$ by showing that any $K$-quasisymmetric group is $K_1$-quasisymmetrically conjugated to a Möbius group. The constant $K_1$ is a function $K$.


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Additional Information

Vladimir Markovic
Affiliation: University of Warwick, Institute of Mathematics, Coventry CV4 7AL, United Kingdom
Email: markovic@maths.warwick.ac.uk

Received by editor(s): December 15, 2004
Published electronically: January 25, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.